Tampere is easily accessible. There are excellent flight connections to Finland from all parts of the world. Several international airlines offer regular flights to Helsinki, the capital of Finland. There is a local train stopping at Helsinki Airport that you can take to Tikkurila station and change there to a long-distance train to Tampere (train connections within Finland are found HERE).
Besides the train connections, there are very good long-distance bus connections from Helsinki Airport to Tampere. There are also several daily connecting flights on week-days to Tampere and vice versa (see Finnair and Tampere-Pirkkala airport). From Tampere-Pirkkala airport there are good connections to Tampere city as well.
Full priced tickets from Helsinki airport to Tampere cost approximately 20-25 euros. You can check here for possible discounted prices. Taking a local bus from Tampere-Pirkkala airport to the city center costs 5 euros; a taxi fare is likely to be upwards from 30 euros.
You can check the weather forecast for Tampere here.