Any way, these animal "signs" are even more complicated (just as Western astrology is more complicated than the 12 Sun signs would suggest). It's actually a 60 year cycle. The first cycle is of the 5 "elements" - wood, fire, earth, metal, and water - from Chinese philosophy in their masculine (Yang) and feminine (Yin) forms.
As Wikipedia explains: "This combination creates the 60-year cycle due to the least amount of years (least common multiple) it would take to get from Yang Wood Rat to its next iteration, which always starts with Yang Wood Rat and ends with Yin Water Boar."
Two iterations of the 60-year cycle are shown below. We are currently in the cycle which began in 1984. Since the Chinese New Year always begins in late January / early February, it's not enough simply to know the year of your birth to determine your "sign". I wasn't just born in the year of the Ox, I'm a Yin Metal Ox, whatever the hell that means (according to this site, it means I'm confrontational and conceited - maybe there is something to this after all!).
Modified from Wikipedia's Chinese Astrology page
Why does the Chinese New Year start in January/February and why does it change each year? You may have noticed that today also happens to be the astronomical New Moon (0739 UTC). Not surprisingly, this ancient 60-year cycle is based on a lunar calendar (all ancient cultures basically used lunar calendars).
Technically, it's based on a lunisolar calendar - a lunar calendar that periodically has an extra month inserted (intercalary month) to keep it in sync with the solar year. Two basic rules of this calendar are that the first day of each month begins at midnight on the day of the full Moon and that a year normally has twelve lunar months.
As with all lunar calendars, this causes a problem because the synodic month, or cycle of lunar phases, is 29.53 days long while the tropical year, or time from solstice to solstice, is 365.24 days. Dividing one by the other gives (365.24 / 29.53) or 12.4 phases per year. This means that every 2.5 years, your calendar will be off by one month. This is where the intercalary month comes into play. Every 2-3 years, you insert another month into the calendar. Various rules (which we'll ignore) determine when to insert the extra month.
Generally, but not always for complicated reasons, the Chinese New Year will fall on the second new Moon after the Winter Solstice. Anyway, as one of my former colleagues always used to say, "It's a poor day you don't learn something new!"
So, best wishes for a happy and prosperous Yang Water Dragon year!