If you are arriving via Helsinki-Vantaa airport, the easiest way to travel by public transport to Helsinki city center and to Espoo is by train and metro. Take the circular train (I or P train) and hop off at Helsinki Central Railway Station. The trip takes about 30 minutes. The trains depart every 10-30 minutes depending on the time of the day. To continue to Espoo from Helsinki Cenral Railway Station take a metro to Matinkylä. If you arrive or leave at night, check the schedule beforehand here.
To plan more about the routes and timetables, Journey Planner is a great way to find out the fastest routes!
At the airport car rental desks are on the ground floor between terminals 1 and 2. There is a parking lot at the EPS harbour.