The West Terminal (Länsiterminaali) is served by tram routes 6T and 9, which have stops in front of the Central Railway Station, for example. The 6T runs to the terminal along Bulevardi while the 9 runs via Kamppi.
Tram routes 2 and 3 take you to the Olympia Terminal in the South Harbour (Eteläsatama). You can hop on e.g. at the Central Railway Station. The tram 2 runs to the terminal via the Market Square and the tram 3 runs via Bulevardi and Eira. At peak times also tram 1A serves the Olympia Terminal.
The Katajanokka Terminal is served by tram 4T, which only runs during the departure and arrival times of passenger ferries. Tram 4, which runs throughout the day, also goes close to the terminal. You can hop on the trams 4 and 4T, for example, at the stops in front of Lasipalatsi and the Stockmann department store.
You are advised to buy your ticket in advance. The more people purchase their tickets from the driver, the longer it takes for the tram to move on. You can purchase a ticket, for example, at the ticket machine located at the tram stop in front of the Central Railway Station. There is a ticket machine also at the Lasipalatsi tram stop.