(written from a Production point of view)
The Galileo-type shuttlecraft, representing the Galileo and Copernicus, was designed by Nilo Rodis and Andy Neskoromny, the Art Director and Set Designer for Star Trek V: The Final Frontier respectively. (Star Trek Encyclopedia, 3rd ed., pp. 184-185). They abandoned the grand vision Andrew Probert originally had for the refit-shuttlebay, and instead revisited Matt Jefferies' original design vision thereof and its accompanying Class F shuttlecraft that went with it, albeit in a upgraded version.
Full scale exterior mock-ups
For the first and only time a full-scale Constitution-class shuttlebay was constructed with two accompanying full-scale mock-ups of the Galileo-type shuttlecraft, and tailored on Jefferies' original vision, as the elaborate vision of Probert was not called upon. Two full-scale exterior mock-ups were built for the film, the Galileo and the Copernicus, with only the Galileo endowed with a fully detailed interior as well.  Cinematographer Andrew Laszlo construed a key sequence with the 8,000 pound (empty) mock-up in Star Trek V: The Final Frontier as follows, "We actually landed the craft by suspending it from a huge construction crane. Not only does it land on the sand dunes, but a second later, the rear hatch opens and out pop a bunch of marines, who leap over the camera, followed by the crew of the Enterprise. We did that in a single shot! Everything becomes very difficult when you work in the sand – vehicles can't move, especially those that can transport and then lift a very large 8,000 pound object. Although this difficulty was foreseen, even with the greatest foresight, certain things can and will go wrong, especially in the course of a motion picture being photographed on sand dunes. Just turning the shuttlecraft around to accommodate another camera angle meant bringing the crane in, picking the craft up, turning it and having the crane clear out of the shot – it took about an hour and a half." (American Cinematographer, issue July 1989, p. 61)
Stored away on the Paramount Pictures lot after use in The Final Frontier, one of the full scale mock-ups received a new lease of life as it was later modified to represent the Type 6 shuttlecraft in Star Trek: The Next Generation. (Star Trek Encyclopedia, 3rd ed., p. 185) Rick Sternbach recalled, "Two full size shuttles were built, IIRC, with one being reworked for TNG. Chopped about six feet out of the middle, got new pods, and some side windows. Both of the original set pieces were weather damaged, but the one we used on TNG was, of course, the less trashed. Exposure to the elements has taken its toll on a number of pieces stored outside over the years; the TMP travel pod was totally trashed by the time we got to the studio for TNG." 
The second full-scale mock-up eventually also received a refurbishment in the form of added weathering, updated signage and added cockpit side windows to represent the Hawking, slated for use in Star Trek Generations in a scene where Jean-Luc Picard is picked up near the end of the film. The scene however, was not used for the theatrical release. (Star Trek Generations (Special Edition) DVD, disc 2, deleted scenes–special) The mock-up was retained for a while by the studio as it was stored on the back lot of Paramount Pictures for several years. At the beginning of 1998 it was very briefly considered for use as an USS Enterprise-E shuttlecraft cockpit in the upcoming feature Star Trek: Insurrection, but due to years of neglect the mock-up had deteriorated considerably and was deemed unfit for use, and the producers decided to go for a redressed Danube-class cockpit set instead. (Star Trek: Action!, p. 234) Ironically, the mock-up was refurbished later that year for inclusion as a tour exhibit, re-dressed as the Hawking, albeit non accessible for the public, appearing in the 1998-1999 Star Trek World Tour, but has not been sighted since, having been most likely struck. wbm
Its limited number of appearances in the Star Trek franchise notwithstanding, the prominent presence of the Galileo-type shuttle in The Final Frontier, eventually sparked the manufacture of more scaled studio miniatures for the type that any other type of shuttle within the franchise. Apart from the full-scale mock-ups, no less than at least six models were known to have been constructed, of which five have been used as production assets.
The 2½ foot studio models
Regardless what Associates and Ferren, the company responsible for the visual effects shots for The Final Frontier, had in mind originally, the construction of a motion control photography model for the (space) flight sequences of the Galileo-type shuttlecraft was never in doubt, as the full-scale mock-ups were simply too large and too heavy for use in the production of shots of this kind. Instead Ferren sub-contracted Gregory Jein, Inc. to construct a motion control photography studio model. Jein recalled, "We built the 2½ foot shuttle using plexiglass slab construction. After filling it with foam and turning out a finished piece, we then molded it, even though we ended up only making one of this size." (American Cinematographer, issue July 1989, p. 79) Constructed at 1/12 scale (or 32 inches), Dana White was among Jein's team who helped with the construction of the model, working from the blueprints used for the full-scale mock-ups. (Cinefex, issue 42, pp. 51, 53) Jein's company also constructed a in-scale shuttlebay maquette that went with the model for the exterior approach shots.
After its use in The Final Frontier, the services of the model was again called upon for usage in Star Trek Generations. (Cinefex, issue 61, p. 77). Like its big full-scale sister, the model was modified with additional weathering, adjusted signage and added cockpit side windows to represent the Hawking. Unlike its big sister it did made an appearance in the theatrical release as said shuttle. The model escaped the 2006-2008 wave of auctions and was instead retained, as the Hawking, by the studio to function as a tour exhibit, appearing in tours like Star Trek World Tour, Star Trek: The Exhibition and Star Trek: The Adventure as late as 2011. 
A second 2½ foot model showed up as Lot #181 in the Profiles in History's The Ultimate Sci-Fi Auction of 26 April 2003, estimated at $10,000-$12,000. That model turned out to be a copy Jein made for his own collection that was on loan to the Orlando, FL., branch of the Planet Hollywood restaurant franchise, where it was photographed in the fall of 1996 by Star Trek studio model aficionado William S. McCullars, who published the pictures on his now-defunct website "The Idic Page". wbm The model was misrepresented in the auction catalog as "used for special effects sequences" (p. 56), since the actual model was still in the possession of the studio and since the offered-up model was endowed with the signage "7" (no doubt Jein's subtle homage to the signage of the original Class F Galileo), instead of "5", as used in The Final Frontier. The model was acquired by Microsoft's co-founder Paul Allen for a winning bid of $8,000, and is currently residing in his Seattle, Washington-based Science Fiction Museum and Hall of Fame.  That model has never been used as a production asset.
The camera test model, aka Guido-II
Initially it was hoped that all the flight-deck sequences, and most notably the crash scene, could be done using the full-scale hangar deck set and the Galileo-type shuttlecraft mock-ups, but as cinematographer Andrew Laszlo ruefully noticed, "To do the effect practically on stage would have involved a bit of wire work, but to try to suspend a shuttlecraft that weighed in excess of 8,000 pounds would have not required wires but cables, which certainly would have photographed. It would have required reinforcing the ceiling of the stage to support that weight. We thought of attaching the shuttlecraft to the boom arm of a large crane as we did for the landing on location in the desert, but unfortunately below this stage was Paramount's antique furniture collection which contains such valuable pieces that not even a standard crane is permitted on that studio floor." (American Cinematographer, issue July 1989, pp. 66-67) Reluctantly, because of problems caused by matching frame-rates involved with miniature filming and live-action (set) filming, the latter differing from the former, the decision was made to have the crash sequence done as miniature effects. In order to alleviate the frame-rate matching problem, a larger scaled miniature of both the shuttle as well as the shuttlebay was deemed necessary, in this case a 1/6 scale.
Once the decision was made and commissions were sent out to have both the 1/6 scale shuttlebay and shuttlecraft models made, intermediate camera test models of both shuttlebay and shuttle were constructed, in anticipation of the final products. Motion Control Expert Peter Wallach said, "Prior to launching this $10,000 shuttle at a $100,000 shuttlebay, we built the "Guido II"–a plywood mockup of the shuttlecraft–which we fired a number of times to determine the best velocity and camera speed for the pyro as well as the scale. One of the main reasons some wanted me to shoot the crash motion control was they were concerned we'd break the model doing it our way(...)" (American Cinematographer, issue July 1989, p. 80) The Guido-II was embellished with K't'inga-class warp engines taken from AMT model kit no. 6682. Both models and the test performed are featured on the Star Trek V: The Final Frontier (Special Edition) DVD, "Pre-Visualization Models" special, disc 2.
The five-foot studio models
The 1/6 model decided upon, and of which three were eventually constructed, were mostly built by Associated and Ferren's own model shop headed by David Sharp, though closely supervised by Gregory Jein, Inc. and with input from some of its employees, among others Warren Riggs. The late decision left Jein no other choice as to delegate some of the work to Associates and Ferren, as he was also responsible for the construction of a like-scaled shuttlebay maquette. Jein recalled, "We needed three of the five foot models – one for the crash sequence which required pyrotechnics and breakaway engine pods, one for motion control and one for a shot of thew craft parked in the shuttlebay of the Enterprise. It was only after the fact that they decided they wanted the engine pylons to break off – which wasn't originally budgeted – so we made a mold of that part and cast them out of rigid polyfoam so the pyrotechnics guys in New York could pack them with whatever they wanted. We used magnets to attach the pylons to the body so they would fly off from the impact of the explosion, which seemed like a quick, foolproof way to do it. The shuttles weren't hard to paint – they were basically one color." (American Cinematographer, issue July 1989, p. 79)
Jein's remark notwithstanding, it did belie the time-stress he and his company were under, as he also solicited help from an acquaintance, David Merriman, Jr., to help out with the construction of the five-feet Galileo-type breakaway nacelles. Merriman recalled, "I was instructed to make the warp engines thin walled GRP structures. Our work was to conform to the details outlined in an information package Greg was overnighting to our location. I didn't know it at the time, but the parts we produced would be packed with explosives and weakened in specific areas to break upon impact with the hangar deck. (...). Our task was three-fold: produce a master (an upper and lower half) of the warp engine, produce a production mold-tool from which to make the warp engine model parts, and produce three sets (six units) of shuttle warp engines." Merriman continued to describe how he managed to construct the asked for parts under extreme time pressure out of sugar pine, Bondo and assorted plastics. It was Merriman's very first uncredited (being sub-contracted by Jein) contribution to the Star Trek franchise. He added:
"Late the next morning a Fedex package arrived from Greg and Ellie and I sat down to examine the blueprints. However, there were no drawings at all, not even a sketch! Just an unusual small scale shuttle warp engine with a post-it-note stuck to its top saying: "build 2X". That was it! Build the things twice the sample provided... period.
I lofted off the dimensions of the sample model with proportional dividers and quickly had a working drawing of the warp engine laid out to the correct size. A trip to the local lumber retailer secured a nice piece of kiln dried Sugar Pine. We were ready to Rock!
By evening time we had the wood cut to rough shape and we set about contouring thew ends with rasp and sandpaper. Not much of a challenge at that point, but there was the matter of the recessed details on the ends and sides of the master to contend with. Those would take a few days to work out.
Within those areas of the master that received the ridged 'ripple' pattern, I first routed out a suitable sized cavity and then laid in lengths of acrylic rod. The perimeter of the recessed areas were framed with suitable cut pieces of plastic sheet. All seams were filled with Bondo automotive putty (...) and worked smooth with file and paper.
The upper and lower wooded shuttle craft warp engines masters were then given liberal amounts of Fill N Sand Gray 131S auto primer (...), sanding between each coat. When finally worked to an unblemished finish, the wooden masters were mounted on a board and a set of fiberglass tools laid up. These tools later formed the GRP copies need by Greg and his crew to complete the big shuttle craft miniatures then being assembled in Los Angeles." (Sci-Fi & Fantasy Models, issue 29, pp. 54-55)
When it came to filming the sequence Wallach commented, "Though we did some 75 shots using motion control, it was my belief you can't do a crash convincingly using motion control, so we built a giant slingshot made from two 22' rails and a sled with roller-skate wheels on it. One has to be flexible with motion control and realize that there's a time to use it and a time not to. One should never lose sight of the fact that a simple rubber band can be a lifesaver. In this case the "rubber band" was a couple of two ton garage door springs cocked back by a three and a half ton winch. We pulled this slingshot back varying distances.(...) My attitude was just to put a little more fiberglass in it and catch it so it wouldn't break. We were having so much fun doing it, we wound up doing six takes in all, and in six takes there was no damage to the model. It was just a paint job away from being ready for the next take. We only needed about 45 minutes between takes." (American Cinematographer, issue July 1989, p. 80) Yet it did not came off without a hitch, as Merriman reiterated, "As it later turned out, the first two attempts to get the shot failed and two of the miniature shuttles [sic: what he meant were the pair of nacelle models] were badly damaged. Only on the last take-using the last model shuttle built for the shot-did they get the desired results." (Sci-Fi & Fantasy Models, issue 29, p. 54)
None of the three five-foot models, constructed out of cast resin and glass fiber with plastic details, measuring 60×27×16 inches (without engines), were ever used again as production assets. The Copernicus model, retained by the studio ever since, was almost immediately afterwards released for public relation purposes, making its debut in the Star Trek: The Exhibition of 1995, and has been included in every exhibition from then forth, as late as of 2011. The two other five-foot models were less fortunate and eventually turned up in 2006 as auction items. Both were offered up for sale in the 2006 Christie's, New York, 40 Years of Star Trek: The Collection auction. One, the model without its detachable engines, was offered as Lot 986 , estimated at $1,500-$2,500. It sold on 7 October 2006 for $12,000 ($14,400 with premium). The five-foot complete Galileo was auctioned off the same day as Lot 987 , estimated at $2,000-$3,000, selling for $9,000 ($10,800 with premium).