This post for stackexchange is an even better explanation of how they came to December 21, 2012 for the end of the Mayan long count calendar.

Conclusion:

yes, the Mayan calendar did not include leap days. But, it didn’t need to, since they didn’t have anything to do with solar years. In fact, as you can see, the closest equivalent Mayan period to a solar year, a tun, is only 360 days — already five days off.

In a nutshell you can just figure out what day on our calendar equals day zero on the Mayan calendar. The article says that day is: August 11th, 3114 B.C.

The entire Mayan calendar is 1,872,000 days long. So you just start at August 11, 3114 B.C. and start counting of those 1.8 million days. Yes, we counted here at bilocation and indeed, you come up with December 21, 2012.