The time since the Big Bang is estimated by extrapolating the observed expansion back in time. It is sort of like a “word problem” in high school mathematics – if a train is traveling at 50 mph and is 200 miles from the station, how long has it been traveling? There is also evidence based on fluctuations in the cosmic background radiation and data that comes from the galaxies. All of these converge on the same date.
Currently it is estimated that the Big Bang took place 13.73 ± 0.12 billion years ago.
At one time, based on available data, it was estimated that the Earth was older than the universe! The Earth’s age estimate, 4.55 billion years, was based primarily on radiometric dating. The universe’s age was based on the sorts of calculations I just described. More recent and more accurate data taken primarily from satellites in space has moved the universe’s age as older than that of the solar system. That, of course, only makes sense.
 http://en.wikipedia.org/wiki/Big_Bang, referenced on January 16, 2009