In the modern calendar, we label all years with B.C. (before Christ) or A.D. (anno domini, or "in the year of our lord"). There is no "zero" year -- in this system, the year Christ was born is 1 A.D., and the year preceding it is 1 B.C.
This practice was first suggested in the sixth century A.D., and was adopted by the pope of that time. It took quite a while for it to become a worldwide standard, however. Russia and Turkey, for example, did not convert to the modern calendar and year scheme until the 20th century.
One interesting side note: Because of a variety of changes and adjustments made to the calendar during the middle ages, it turns out that Jesus was most likely born in what we now think of as 6 B.C., and likely lived until 30 A.D.
Besides B.C. and A.D., some people use B.C.E. (for "before common era") and C.E. (for "common era").
For more information on time and related topics, check out the links below.