By Taiwan High Speed Rail (THSR)
All THSR trains stop at THSR Taichung Station. There are frequent trains from Taipei (50-60 minutes, NT$700) and Zuoying in Kaohsiung (42-58 minutes, NT$790). From the connected TRA Xinwuri Station you can then take a shuttle train into the city center, where the main Taiwan Railway station is (12 minutes, NT$15).
By Taiwan Railway (TRA)
As well as frequent local trains to and from Taichung Station, there are also express trains from cities such as Taipei (100 minutes-2 hours, NT$375) and Kaohsiung (2 and a half hours, NT$469). While not as comfortable as the high speed trains, these express services are cheaper and take you right into the city center.
By highway bus
Bus services are provided day and night to and from the city. Prices are cheaper than trains, with tickets around $250-$300 from Taipei.
By air
Taichung does have Taichung International Airport, but flights are usually much more expensive than Taiwan Taoyuan International Airport near Taipei. Getting here via the Taiwan High Speed Train from Taoyuan is a much better option.