The nearest airport is the Helsinki Airport, which has good connections to all the European capitals and to the USA and Asia. The local bus number 615 takes you from the airport to the Helsinki Central Railway Station in approx. 30 min. The bus leaves from right outside the arrival terminals, and a single ticket costs 5 euros.
The Finnair shuttle bus is a direct non-stop connection from the airport to the Central Railway Station; its slighty more expensive than the local bus. There are also taxis available at the airport, including some special Airport Taxis or Yellow Taxis, which have cheaper rates for groups of clients going in the same direction.
Apart from flying, you can also arrive in Helsinki by sea from Sweden, Estonia, Germany and Poland. The ferries are operated by Viking Line, Tallink Silja and Finnlines.