If you want something that can convert the Date to an actual Star Trek Stardate here is a convert:
http://www.hillschmidt.de/gbr/sternenzeit.htm
The year is 2393
Our current day depends on what your perspective is. I usually advance the time depending upon what CJ says now, so if there is a time change of say 6Hrs. My log will fall within a 6 hour time. Usually prior to the sim, or right after the last. You can watch my logs for queues. Usually I advance time as long as the sim runs. So if we go an hour, I advance an hour, if we go more. I usually mirror it to within a 30 minute window. If there is a time change in sim like we advance an hour I try and remember to work that into the time calculation. It does not have to be perfect. You can always check my logs for a good reference. Or previous reference.
You can also use the calculator to convert a Stardate to a Date. Just use the other field on the lower half.
So the next sim will pick up essentially IC time of December 7, 2393 @ around 0500 or later which is +6 Hours from the time our last sim Ended in game.
The Previous Date was December 6, 2393 @ 22:25:45 which was shortly after our sim Ended. By maybe 30mins - 1 hour after.
I hope that helps.