It is, perhaps, an appropriate time for this blog to come back to life, because this Thursday will be the first day of the New Year in the Chinese calendar.
The Chinese calendar is a type of calendar known as a lunisolar calendar, since it incorporates both the phase of the moon and the season of the solar year. To understand the difference between a lunisolar calendar and a purely lunar calendar, note that while a solar year (the time from one spring equinox to the next) is around 365.24 days on average, a lunar month (the time from one new moon to the next) is around 29.53 days on average, and so the solar year does not have a whole number of lunar months in it; a lunar year consisting of 12 lunar months is about 11 days shorter than a solar year. Hence, a purely lunar calendar (such as the Islamic calendar) will exhibit some "drift" in relation to the seasons, and festivals dated by such a calendar will be celebrated at a slightly different season every year.
A lunisolar calendar avoids this drift by adding an extra month — an intercalary month — every so often. Since the deficit per solar year is around 11 days, which is around a third of a lunar month, this extra month needs to be added roughly every three years. There is an obvious parallel here with the Gregorian calendar's custom of adding an extra day to the end of February every four years or so, to deal with the discrepancy between the solar year and the 365-day year. The next intercalary month in the Chinese calendar will begin on 21 March 2012, lying between the fourth and fifth lunar months.
The method of calculating the Chinese calendar is actually quite complicated, and has changed a number of times over the centuries. Helmer Aslaksen, a mathematician working at the National University of Singapore, has a fairly comprehensive page on the subject. For those who'd prefer to avoid the maths, he links to an online tool for generating Chinese calendars for particular Gregorian months/years; the code behind this is also available as a command-line program, though I haven't tried it out, as I already have the Perl Calendar module installed, which comes with its own command-line tool, cal.pl:
kake@the:~$ cal.pl -c 2 2011 2011年2月 辛卯年正月大3日始 Sun 日 Mon 一 Tue 二 Wed 三 Thu 四 Fri 五 Sat 六 1廿九 2三十 3正月 4立春 5初三 6初四 7初五 8初六 9初七 10初八 11初九 12初十 13十一 14十二 15十三 16十四 17十五 18十六 19雨水 20十八 21十九 22二十 23廿一 24廿二 25廿三 26廿四 27廿五 28廿六
Note, above, the entry for Thursday 3 February; 正月 (zhēng yuè), which denotes the first month of the year. Most of the other entries are numbers, for example the entry for Wednesday 2 is 三十 (sān shí), which means "thirty", this being the 30th day of the final month of the preceding year.
There are also various online calculators for a quick online conversion of a single date, for example Henry Fong's hundred-year calculator.