Just a heads up for anyone planning to do the "Helsinki Tram Tour" described in Rick's Scandinavia book -- the routes for trams 2 and 3 changed yesterday and the two lines no longer make a figure eight. To get roughly the same trip, take the 2 from the market square as suggested. It will not go by the train station as described, but you will see that later on anyway. Get off the 2 at Töölön halli. Get on the 3 there and continue the journey as described in the book.
The tram ticket you buy at the beginning is good for an hour, so you should not need a second ticket when getting on the #3 tram unless you decide to walk to the Sibelius monument or the Olympic stadium before catching the next tram. We bought day passes at the TI and spent the morning at Suomenlinna and then used the trams as a hop-on-hop-off tour in the afternoon, and that worked quite well.