Getting around Koh Samui is easy, you can either rent a motorbike for roughly 200 Baht a day, or hire many different forms of jeep. You officially require your drivers license to rent a vehicle, so make sure that you bring it. There are also jeep taxis that cruise the streets looking for passengers, it will normally cost you just 20 Baht to go anywhere within Chaweng, although the prices can increase after midnight to up to 50 Baht, especially if you are leaving a night spot.
The best way to get aroud the island is by motorbike. for 100-150 B/day you can hire a Honda dream. You can easily drive round the island on one day. Make a stop at Bophut and Menam beach. Relax and enjoy yourself! Make a stop in Nathon for shopping and dinner. But never drive if you have been drinking alcohol, there are too many traffic accidends anyway!
If you drive on the hill roads, be careful! Some roads are really bad!
The cheapest way travel on the island is using motor bikes. If you never used before. This is a little bit dangerous. I saw many accident. If I remember good, rent a bike was 150 Bat and you have to pay for gas extra. The gas is not so expensive. Ko Samui island is not so big. You can get free map for travelling. From Beach to beach. If you are lucky you can find secret beaches.
Renting a motorbike is one of the cheapest transportation in Samui rates start from 200baht per day depending the season and someone can find from 100cc -900cc