How to get from the airport to the city centre?
When you have arrived to the airport, after the luggage hall, follow the signs to the train (railway station) and take escalator or lift down to the station. Buy a ticket (regional ABC, about 5€,) from the ticket automates which are located on the platform.
From there goes two trains (I and P) to opposite directions. However, both goes to Helsinki Central railway station, every 10 minutes, so you can take which one comes first. (Note: There is no ticket sale on the train).