Bus line 39A and 103 operates between the airport and Tampere city center. More information is available on Tampere public transport website.
The digital timetable
The information of Ryanair bus connection is 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.