Bus is the most convenient and least expensive option. From Taipei Train Station, go to the bus terminal and take the Tong-Lien Bus (統聯客運), Kuo-Kuang Bus (國光客運). Tickets cost from NT$100-350, depending on what day of the week you travel on. Buses depart several times an hour from the early morning through evenings and the entire ride is about three hours long.
All Taiwan High Speed Rail (HSR) trains between Taipei and Kaohsiung stop at Taichung. The High Speed Rail station is located on the outskirts of Taichung. You can take a regular train between the two stations in about six minutes, in addition, a free bus is available to take HSR passengers downtown, to the universities, etc.
In addition, Taichung is a major stop along the Western Line with all north and south bound trains a making a stop here. Express trains (ZiQiang) are NT$375 from Taipei and NT$470 from Kaohsiung. Midrange ticket prices (Jukuang class) typically run around NT$289 from Taipei or NT$363 from Kaohsiung. The entire trip takes about three hours from both Taipei and Kaohsiung. The Western Line station is located in central Taichung.
Taichung airport operates mostly as domestic hub, though it does also offer a limited international service to neighboring counties. A flight to Taipei takes 40 minutes, although air service to Taipei has been cut back lately as the High Speed Rail is generally a faster and more convenient way to get there.
An international terminal is being built currently in Taichung and is going to be the largest airport in Taiwan and the terminal's floor area is more than 800,000 square meters. This airport is normally compared to the Beijing Capital International Airport T3, The Changi International Airport T3 in Singapore, and other big airports around the world. This new airport will offer at least 80 airlines and more than 70 restaurants. This airport was scheduled to be finished by the end of 2009. However, as of early 2011 this expansion has not yet been completed.