By ship
Yes, there is a waterway between Tampere and Hämeenlinna. At summer it can be the most enjoyable way to travel, while the views at the lake Vanajavesi are at their best. The trip can be quite long though. Finnish Silverline (http://www.finnishsilverl...) offers cruises, which take 8 hours one way.
By train
As Hämeenlinna is situated at the most important railway (http://www.vr.fi) of Western Finland it's well connected with Helsinki and Tampere as well as cities further north, like Vaasa, Oulu and Rovaniemi.
By car
Exactly 100 km north from Helsinki with the motorway 3 E12. The nearest major city and airport is Tampere, about 75 km to the north. Road number 10 From Turku to Lahti also goes near the city.
By bus
Buses from Helsinki to Tampere stop at Hämeenlinna.