There are various levels of service from 2nd or 3d class coach to 1st class sleepers. You may wish to use it overnight as a substitute for regular accommodations. This is often done on overnight ferrys. On shorter trips, you can still use local railroads or the bus system. Often buses provide a more scenic route and serve less traveled areas.
Car rental can be economical if two or more are traveling together.
Often there are very delightful bike trips organized by various Hostels or local bike clubs. You can take your own bike, but shipping is expensive and a hassle to carry with you. You can rent locally. There are a number of well marked trails, especially in Europe. Typically, we discourage hitchhiking, especially for females and absolutely NO if she is alone.