We arrived at Taoyuen International Airport at around 3.30pm. You can either get to Taipei by cab (I think it’s around NTD 900 or so) or take a bus to Taipei, a popular one to take would be the “Free -Go” bus, also known as “飞狗巴士” in Taiwan.
When you exit from the arrival gate, you will see sign boards that will lead you to the bus station.
Then, keep going straight, and make a turn on your right and go down the escalator.
At the end of the elevator, turn right and you will be able to see bus ticket counters from various companies. There are bus schedules on the wall as well.
So just buy your ticket and go! A lot of the hotels in Taipei are working with the bus companies, so check with your hotel to see which company they are working with, and the bus will take you right to the door steps of the hotel.
We stayed in Neijiang Hotel in Taipei. We took the Free Go Bus (which translates to “Flying Dog” in Mandarin) for NTD 140 per person. The bus took us to Taipei, where we changed to a connection bus . The connection bus took us directly to the door of Neijiang Hotel (with a few stops along the way at other hotels). The total journey took about 1hour. Alternatively, you can also take the bus to Taipei Main Station and take a cab to your designated hotel. All the bus companies will go to Taipei Main Station, so you don’t neccesarily have to take Free-Go Bus. The fare from the airport to Taipei Main Station is NTD 120. The fare from Taipei Main Station to Neijiang Hotel was around NTD 100.
The bus came quite frequently, I think one bus every 15 or 20 minutes or so. We only had to wait 10 minutes after purchase of ticket :)
When you are departing from Taiwan, you can ask the receptionist to pre-book the bus from the hotel to the airport as well.
Website for Freego Bus http://www.freego.com.tw/
Website for Taoyuen International Airport http://www.taoyuan-airport.com/english/index.jsp