This is a big island, only second in size to Phuket and though it is gorgeous to stroll along the beach or go on planned hiking trails, getting from one point to another will see some distance and steep hills to be kept in mind. Scooters, the 1st choice of transport for tourists and Thais alike can be rented for 200-300 baht per day from basically any Koh Chang hotel.
Renting a small jeep is also a good option for, especially when you want to tour around the island and explore the sights where a scooter cannot go. Jeeps are able to negotiate terrain a taxi or other mode of transport would not necessarily be able to. Car rental agencies would be able to offer jeeps for rent from approximately 800 Baht per day.
Another way of getting from A to B cheap and quickly is by Songthaew taxi. These pick-up trucks, modified to carry passengers with two rows of benches fitted in the back and a canopy on top and open at the sides, travel up and down the west coast. If you want to travel the east of the island which is less developed there will be no public transport available however and you will need your own wheels, jeep or scooter.