Blood screenings were a procedure that attempted to detect Changelings by drawing blood from the subject. When a Changeling's matter is removed from its central form, it reverts to its liquid state.
Odo first suggested the procedure in late 2371 when a Changeling hijacked the USS Defiant. However, the tactic failed because the Changeling had replaced Julian Bashir, who performed the screenings, and he was able to frame Michael Eddington as the Changeling instead. (DS9: "The Adversary")
By early 2372, the Klingons also used blood screenings to detect Changelings, but their method was cruder — they simply used an available blade (such as a d'k tagh) to break the skin and allow some blood to escape. (DS9: "The Way of the Warrior") It was not discovered until much later that a Changeling was impersonating General Martok, and was able to evade the blood screenings. (DS9: "Apocalypse Rising")
When the Changelings threatened Earth in mid-2372, Starfleet Command adopted an official policy, recommended by Benjamin Sisko (acting as temporary head of Starfleet Security on Earth) requiring weekly blood screenings of all Starfleet personnel and their immediate families. (DS9: "Homefront") However, Admiral Leyton managed to fake a blood screening to frame Sisko as a Changeling when Sisko was trying to expose Leyton's attempted coup against the Federation civilian government. (DS9: "Paradise Lost")
Despite their apparent ineffectiveness, blood screenings continued to be used on occasion as a stopgap measure to guard against Changeling infiltration. (DS9: "In Purgatory's Shadow", "By Inferno's Light")