Information on the Maya calendar is rather easy to come by, given it's probably the most popular aspect of their culture. Only trouble is discerning actual information from the pseudoscience. If someone talks about 2012 as being the apocalypse or even the end date for the entire calendar, then you can automatically dismiss it.
This site is actually pretty fun to use while containing a lot of intriguing info. Personally I think it's better than the Gregorian calendar, it's certainly more organized and consistent. Every month has the same amount of days, for starters. 20 days a month, 18 months a year, plus 5 unnamed days at the end that are considered bad luck. I've also heard the calendar is self-correcting as Maya astronomers were aware that a year isn't exactly 365 days. There are also in actuality 3 calendars you have to be aware of. There's the Haab, the civic calendar that has the 365-day years. There's also the Tzolk'in, which is the ritual calendar containing 260 days a year. The Tzolkin I've heard is still in use by some Maya farmers. Combining the Haab and Tzolk'in gets you the Calendar Round of 52-years. This Calendar Round is considered pretty significant, and was the longest measure of time by the Aztecs, but the Maya also had what's now called the Long Count calendar, which is the linear count of years from their (rather arbitrarily picked) start date of the current cycle extending on infinitely. There are multiple divisions of time within. The katun is particularly significant, a katun being roughly 20 years. The baktun (20 katuns, the Maya used a vigesimal number system) is what's getting a lot of attention now because the 13th one starts in a few months on December 21st and New Agers think it's the end of the world because New Agers generally tend to be crazy.
To elaborate on the differences between the Haab and Tzolkin beyond number of days, I shall explain more. The Haab functions in a civic or secular manner as I explained before and functioned more like our calendar. Though days were counted differently. The months were counted as beginning on the 0th of that month, which was shorthand for saying the "seating" of the uinal/month. Therefore a month would end on the 19th day rather than the 20th. They also held festivals every single month (meaning 18 festivals/holidays a year, and some could last for days, a lot of time to party!). Today for example is on the Haab calendar 4 Mol. That means the local carvers should be making images of the gods and preparing them with the proper ceremonies and rituals. Seems they've been a bit derelict in their duties though... As for the Tzolk'in, it decides more esoteric manners and Tzolk'in days each have their own flavor. They are also counted different. There are no months, instead there are 20 different names for Tzolk'in days and they are counted in order until after the 13th one, where the count begins anew with the next day. Today on the Tzolk'in is 2 Imix, meaning tomorrow is 3 Ik', then 4 Ak'bal and so on until 13 Eb, then the next day is 1 Ben followed by 2 Ix and so on. In any case, the Tzolk'in day can determine what is most auspicious and the likely portent's of a child's life. Outside of the Maya area children were often if not usually initially named after the Tzolk'in day they were born on, though the Maya don't seem to have done that often.