The most convenient way to reach Tampere is to fly first to Helsinki (Helsinki-Vantaa airport) and then continue by taking a train.
When in Tikkurila train station, change to a pendolino or to intercity train that takes you to Tampere train station.
From VR website you can buy both commuter train ticket and the long haul train tickets at the same time. Here is the link to VR shop: https://www.vr.fi/cs/vr/en/frontpage
Write Helsinki Airport and Tampere to the boxes shown on the web page (from/to). Then choose the departure time and date and proceed and the page will guide you onwards.
Tampere is easily accessible by train from all over the country. From Helsinki, regular trains operate to the city centre in less than two hours. Services run approximately once per hour. The new train track has been built to run through Helsinki-Vantaa airport. Timetables and tickets can be bought here.
From Helsinki-Vantaa airport you can aslo take a bus to Tampere. Timetable from Helsinki-Vantaa airport to Tampere can be found here.