(covers information from several alternate timelines)
The Martian colonies are one of the oldest colonies of Humankind and were established in 2103 on the planet Mars. Among the pioneers who settled the first colony were some of Jean-Luc Picard's ancestors. (Star Trek Generations; DS9: "In the Cards"; VOY: "The 37's")
Having been completed in 2012, the Millennium Gate on Earth served as a model for the first colony on the red planet. It pioneered many new technologies and scientific principles like a coverage by highly-reflective solar panels and being constructed as a self-contained biosphere. (VOY: "11:59") The Fundamental Declarations of the Martian colonies were an important step in the pursuit of individual rights. (TOS: "Court Martial")
The flag of the first of the Martian colonies was inspired by a velvet painting of a matador, according to Quark. He was trying to auction it off at the time, however, so the claim may well be overblown. (DS9: "In the Cards")
In 2155, when a xenophobic faction of Humans known as Terra Prime took over the verteron array, Starfleet intended to destroy the array rather than let the terrorist organization carry out their attack on San Francisco. Destroying the array threatened to destroy a portion of Utopia colony, an indication that the two were in close proximity to one another. The colony had at least one hospital as of 2155. (ENT: "Demons", "Terra Prime")
Known citizens include Lieutenant Mira Romaine, a crewmember of the USS Enterprise who was born at Martian Colony 3, and Simon Tarses, crewmember of the USS Enterprise-D. (TOS: "The Lights of Zetar"; TNG: "The Drumhead")
Although Harry Kim stated in VOY: "The 37's" established that "Mars was colonized by people from Earth in 2103", ENT: "Terra Nova" establishes that Mars was colonized prior to 2069 with the building of Utopia Planitia. This seems to make more sense since 2103 is forty years after the warp drive was invented, and after deep-space expeditions like SS Valiant and Friendship 1 and after the Terra Nova colony was established in another star system. The 2103 date may refer to the formal incorporation of the colonies as one body, the year Humans were first able to colonize the planet on a long-term basis, or the beginning of the terraforming project seen in ENT: "Terra Prime".
The buildings representing the Martian colonies in episodes such as "Lifesigns" were built out of garbage cover plates, birdbaths, cat toys, and hair curlers by using the technique "kitbashing". Penny Juday gives some insight in the TNG Season 2 DVD special feature "Inside Starfleet Archives - Penny Juday, Star Trek Coordinator".