What was used before BC and AD?

Some civilizations used BCE and CE which stand for "Before Common Era" and "Common Era"

(Not strictly true. CE and BCE are "politically correct" modern innovations, concocted so that Jews and other non-Christians don't feel left out. No previous civilization has ever used them. After all, the Christian Era was not the "common" era until Christianity became dominant in the West.)

Years

Different civilisations used different methods. The Romans named them after the consuls who ruled in that year, eg The year of Julius and Pompey, the Greeks may have named the year after the victor of the 100m sprint in the Olympics

Rome also reckoned time from the supposed foundation of the City in 753BC, so 3BC would have been 750AUC (Anno Urbis Conditae)

The Greeks also sometimes reckoned from the beginning of the Olympics, supposedly in 776BC, so 356BC (when Alexander the Great was born) would have been the first year of the 106th Olympiad.

Before Christ

Anno Domini (In the Year of our Lord)