(covers information from several alternate timelines)
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 Martian colonies were established in 2103, although settlements on Mars had already existed by 2069. (ENT: "Terra Nova"; VOY: "The 37's") Among the pioneers who settled the first colony were some of Jean-Luc Picard's ancestors. (Star Trek Generations) 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. (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 and his brother, the former a crewmember of the USS Enterprise-D. (TOS: "The Lights of Zetar"; TNG: "The Drumhead")
Although Harry Kim stated in VOY: "The 37's" 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".
The Martian city seen in "Lifesigns" was not referred to in the first draft script. In the episode's final draft script, it was referred to as "a futuristic domed city." According to the Star Trek Encyclopedia (3rd ed., p. 538), it was located at Utopia Planetia. The encyclopedia also noted that it was realized as a matte painting by Dan Curry, based on designs by Anthony Fredrickson and Doug Drexler.