You can get around Koh Chang by taxi, car, motorcycle, scooter or bicycle. The roads are steep and curvy. Drive carefully, especially during or right after rain. For single trips, taxis are the best. You sit in the back of taxis and just hail them on the street. Should you make several trips, it pays quickly with car rentals.
If you want to have guided tours, trekking etc we recommend you to give an email to Thomas, an english speaking guide. The best on Koh Chang. He is also on facebook.