You can travel to Tampere from abroad by flying to Helsinki (Helsinki-Vantaa airport) and continuing from Helsinki to Tampere by train or bus: public transport from Helsinki-Vantaa.
Notice that if you take the train from the airport, you have to travel first towards the city of Helsinki and transfer in Tikkurila. Remeber to buy the train ticket from the station since tickets are not sold in trains.
There are some flights to Tampere (Tampere-Pirkkala airport). The airport is 16 km from the city centre: Tampere public transport.