Passenger trains leave Helsinki twice daily for St. Petersburg, a roughly 3-hour trip, and once daily on an overnighter to Moscow (13 hours). Remember that you need a visa to travel to Russia. To get to northern Sweden or Norway, you must combine train–bus or train–boat travel.
The Finnish State Railways, or VR, serve southern Finland well, but connections in the central and northern sections are scarcer and are supplemented by buses. Helsinki is the main junction, with Riihimäki to the north a major hub. You can get as far north as Rovaniemi and Kemijärvi by rail, but to penetrate farther into Lapland, you'll need to rely on buses, domestic flights, or local taxis.
Note that all train travelers in Finland must have a reserved seat, but it is possible to buy a seat ticket on the train. Special fast trains (Intercity and the Helsinki-Turku Pendolino) are more expensive but also more comfortable. First- and second-class seats are available on all express trains.
Finnish Railways. 0600/41–902; www.vr.fi.
Rail Europe. 888/382–7245; 800/622–8600; www.raileurope.com.