There are two international airports in Taiwan.

Taipei (Taoyuan) International Airport and KHH ( Kaohsiung) International Airport.

A.If you arrive in Taipei ( Taoyuan )International Airport, there are four ways to Tainan City:

1.take the shuttle bus or taxi to Taoyuan High SpeedRail station (around 18 mins ) by rail ( southbound) to Tainan High Speed Rail station (around 80 mins),
then by the shuttle bus or taxi to downtown (around 22 mins)

2.take the shuttle bus or taxi to Taipei DomesticAirport ( around 50 mins ), then by the plane to Tainan Domestic Airport (around 45 mins ), then by the taxi to downtown (around 15 mins )

3.take the shuttle bus or taxi to Taipei railway station(around 50 mins), then by the train (southbound) to Tainan Railway station ( around 4 hrs/ 320 kms)
where in downtown.

4.take the shuttle bus to Tainan city ( around 4 hrs/ 280ksm )

B. If you arrive in KHH (Kaohsiung ) International Airport
1.take the shuttle bus or taxi to Kaohsiung High Speed Rail Station by rail to Tainan High Speed Rail Station, then by the shuttle bus or taxi to downtown.

2.Take the shuttle bus or taxi to Kaohsiung RailwayStation, then by the train to Tainan Railway Stationwhere in downtown.

3.Take the shuttle bus to Tainan City.