Take one of the cabs waiting just by the exit. They are Tallinn Airport's official partners and depending on traffic, should charge about 4-6 euros. Or, you can use the exit downstairs, and take the bus nr 2 or K90 from the leftmost bus stop.
Other people asked questions on similar topics, check out the answers they received:
Other people asked questions on various topics, and are still waiting for answer. Would be great if you can take a sec and answer them