Well they didn’t start year 1 in year 1. I’m not sure any calendars did except the French Revolutionary Calendar and perhaps the Islamic calendar. Most continusous numbering calendars were adopted after the fact then back-dated to some event’s supposed date. Calendars that counted the years of some king’s reign would have been started contemporaneously.
The common calendar now known as the Gregorian Calendar was started after the fact and year 1 is supposed to mark the year of Jesus’ birth. It was started in the sixth century as an aside in the calculation of Easter dates. Most scholars now say that the internal evidence from the stories indicates that Jesus could not have been born any later than about 4 B.C. (which I think is the year of Herod’s death.) I seem to recall that 6 B.C. might be the consensus.
The suffix A.D. you often see appended stands for Anno Domini, Latin for “Year of the Lord”. The B.C. suffix stands for Before Christ. You sometimes see these now as C.E. and B.C.E. standing for Common Era and Before the Common Era.
There is no year 0. 1 A.D. immediately follows 1 B.C. probably because when the B.C. suffix was first used, European mathemeticians still hadn’t adopted the notion of 0 and negative numbers.
Much more information can be found for example at
If you want to search further Gregorian Julian and calendar ar good key words.