Tainan is not a very big city and it has no metro. A good option to move around is the bus (some of them are free), but sometimes it's really challenging if you cannot read Chinese. The taxi is an expensive option if you plan to move a lot. So the best option, if you got a car license, is to rent a bike for about 400NTD (9€) a day. The city is not very complicated, so you'll be able to move easily reading a map.
Take care, the traffic is crazy! Sometimes looks like there's no rules!