According to the Original Series Writer's Guide:
We invented "Stardate" to avoid continually mentioning Star Trek's century (actually, about two hundred years from now), and getting into arguments about whether this or that would have developed by then. Pick any combination of four numbers plus a percentage point, use it as your story's stardate. For example, 1313.5 is twelve o'clock noon of one day and 1314.5 would be noon of the next day. Each percentage point is roughly equivalent to one-tenth of one day. The progression of stardates in your script should remain constant but don't worry about whether or not there is a progression from other scripts. 126
Stardates are a mathematical formula which varies depending on location in the galaxy, velocity of travel, and other factors, can vary widely from episode to episode.
The Writer's Guide for The Next Generation stated:
A stardate is a five-digit number followed by a decimal point and one more digit. Example: "41254.7." The first two digits of the stardate are always "41." The 4 stands for 24th century, the 1 indicates first season. The additional three leading digits will progress unevenly during the course of the season from 000 to 999. The digit following the decimal point is generally regarded as a day counter.
Deep Space Nine began with 46379.1, corresponding to the sixth season of Star Trek:
Star Trek: Voyager began with stardate 48315.6 (2371), one season after TNG had finished its seventh and final season. As in TNG, the second digit would increase by one every season, while the initial two digits eventually rolled over from 49 to 50, despite the year 2373 still being in the 24th century.
Star Trek: Nemesis was set around stardate 56844.9, which is so far the highest stardate to have been mentioned in the Star Trek canon.
To answer the original question, there was never any rule devised by writers to explain what date was used, so one can only assume they used some sort of GMT (Greenwich Mean Time) across the galaxies, based on a focal point (which may or may not have been the Federation headquarters). 126