I’ve seen various answers to how stardates relate to real dates. But is there a general consensus on the correct/most valid answer that holds for all of the various media?
All these quotes are from the Memory Alpha article on Stardates:
The Original Series, the Star Trek Guide:
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. 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.
Direct from Gene Roddenberry:
When we began making episodes, we would use a star date such as 2317 one week, and then a week later when we made the next episode we would move the star date up to 2942, and so on. Unfortunately, however, the episodes are not aired in the same order in which we filmed them. So we began to get complaints from the viewers, asking, "How come one week the star date is 2891, the next week it's 2337, and then the week after it's 3414?"
In answering these questions, I came up with the statement that "this time system adjusts for shifts in relative time which occur due to the vessel's speed and space warp capability. It has little relationship to Earth's time as we know it. One hour aboard the U.S.S. Enterprise at different times may equal as little as three Earth hours. The star dates specified in the log entry must be computed against the speed of the vessel, the space warp, and its position within our galaxy, in order to give a meaningful reading." Therefore star date would be one thing at one point in the galaxy and something else again at another point in the galaxy.
From the Star Trek: The Next Generation Writer's/Director's Guide:
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.
Star Trek 2009 didn't conform to either TOS or TNG-style stardates:
Stardates from the latest film were developed by screenwriters Roberto Orci and Alex Kurtzman. According to Orci, they "used the system where, for example, 2233.45 or whatever means 23rd century, 33rd year of that century, and the .45 indicates the day of the year out of 365 days."  During a Q&A session, Orci restated that a stardate is "the year, as in 2233, with the month and day expressed as a decimal point from .1 to .365 (as in the 365 days of the year)."  A similar reply was posted on his Twitter account: "star date=standard year, with decimal representing day of year from 1-365." 
Orci never said whether leap years end at .366, which would be expected if the digits before the decimal point correspond to Gregorian calendar years, and he didn't explain why stardates 2230.06 and 2233.04 were scripted if .1 is supposed to be the starting decimal. The table below shows stardates from the film.
The page does note that DS9 and VOY used the same system as TNG:
The second digit continued to increase every TV season in other spin-offs as well, even after TNG had ended. Since DS9 premiered during the sixth season of TNG and was set in exactly the same timeframe, stardates on DS9 ranged from 46379.1 to 52861.3. Likewise, the first season of Voyager would've been the eighth season of TNG had it continued, so Voyager stardates ranged from 48315.6 to 54973.4. Star Trek Nemesis, the latest Star Trek story in the 24th century, had a stardate of 56844.9, showing that it took place approximately fifteen years after the first season of TNG.
And finally, throughout the page are comparisons between the Stardate and Gregorian calendars that have popped up in various episodes, notes on inconsistencies, and so on.