Between cities and major towns you can use the trains (http://www.vr.fi) or buses (http://www.matkahuolto.fi). Hitchhiking is uncommon but possible, but be aware that some roads have very little traffic. If you chose smaller country roads, cycling is a possibility and you can camp wild as long as you regard the "jokamiehenoikeus" right to access which states basically "behave".
