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There are 3 ways you can move around Costa Rica:
3- Car rental
In order to choose the right one you have to take some things into consideration.
How long are you staying here, your destination and how much money you want to spend.
If you are having a short trip and you have some cash to spare, or if you have long trip but you want to check as many places as possible you might as well move fast so you can check all the places you want, in that case, try the airplanes. There are two major companies Sansa and Nature Air. You will find maps on their websites which you can use. Also many hotels will pick you up at those places with no charge.
If you have enough time and have an adventure spirit, try renting a car, that way you'll have the chance to check the scenery. Just remember to get a car with GPS, there are very few road signals and it's easy to get lost along the way. The roads are pretty bad, a 4X4 is recommended, drive carefully, slowly and be ready for the unexpected. Don't get directions from anybody, try restaurants, there are many who speak english that can help you. Also never travel at night unless its needed and don't take passengers from the road. My favorite is Toyota Rent a Car, they have cool cars, new ones, and GPS which has the latest map info.
Now if you don't want to drive but still, you want to check the scenery, try the bus. It's the cheapest, takes longer, but you'll get to you destination. Try Gray Line, they are pretty good, local buses tend to get pretty crowded, and depending on the place you are going its not that safe.
Finally, never hitch hike. It's not safe, no one will stop to help you and definitely no one will give you a ride. It's just wasting time and energy to save a few bucks, which in the end will cost you more if you get mugged and loose everything you brought.