We actually don't know how he chose the date, he only recorded his arguments for the dates of particular Easters (or at least, those are the only records that survived).

The most likely method, however, is based on the Gospel of Luke. According to Luke, the word of God came to John (the Baptist) in the wilderness in the 15th year of Emperor Tiberius. This is 29AD (or possibly 27 AD, as he reigned as co-Emperor with Augustus for 2 years before becoming sole Emperor, but that's not how Emperor's reigns were normally dated). Jesus appears in the Gospels to be baptised by John not a huge time afterwards, though no specific dates are given (a few months? A year? Two years? 5? It's not stated). Luke also says that Jesus was about 30 when he started preaching.

So, if John began preaching in 29AD, and baptised Jesus a year or so later when Jesus was 30, that would give you the date of Jesus's birth that Exiguus used.

As you can see, it's not 100% clear, but that's the method that would give this date, and so is the most likely method (if you go by Matthew's nativity story, Jesus would have been born prior to Herod's death in 4 BC, if you go by Luke's nativity story he'd have been born during the census of Quirrinus in 6AD: they don't fit together). But we can't say for certain.