Many overseas placements are in major metropolitan areas which have excellent public transportation.
When your school provides you with accommodations, they are often within walking distance of the school, and if not, they may provide assistance in finding suitable transportation.
Some contracts will require you to have a drivers license or the ability to operate a moped or motor-scooter to travel from site to site. Again, it will all depend on where you are teaching and the contract and country conditions.
Visit the Transportation section included in Oxford Seminars Where You Can Teach for specific countries modes of transportation.