Bus line 1A operates between the airport and Tampere city center. More information is available on Tampere public transport website.
The Ryanair bus connection is operated between Tampere railway station and the airport. Timetables are available on Tokeen Liikenne's website (only in Finnish).
You can also use the Matkahuolto's website to check bus schedules and VR's website to check train connections to and from Tampere.