The easiest way to get around is by car. All roads and bridges are for free and so are also the state operated car boats. The highway system is modern and there is plenty of nice guided de-tours from the main roads. Car rentals is available and almost every petrol station have cars to rent and at airports.If you plan to go from city to city the cheapest way is the coach system. Most big cities have a bus station where you can get information on departures. Swebus Express is the biggest company with connections to most cities and guarantee you a seat. Smaller companies are often cheaper but require you to book. Going by train is quite expensive, but you can find lower fares at some departures. If you are under 26 you can get a cheap last minute train ticket online or at the station.  Flying are getting cheaper but most flights go through Stockholm. SAS offers very cheap stand-by tickets for if you are under 26. New airlines are starting all the time so look around for your options. Hitch hiking is not very common but is relatively safe. An international student id card can give you plenty of discounts however some places require a Swedish one.