There are basically 2 main options for Public Transport around Koh Samui either Songtaews (covered utilities) or metered Taxi`s.

Songtaews circle the island 24/7 obviously the later the harder they are to find but they are the cheapest EG  a ride up or down the main beach road of Chaweng will cost you 20 baht pp daytime then 30 baht of a night.If you want to catch a songtaew just stand on the side of the road & signal & to exit either press a buzzer on the roof or bash on the side or roof near your destination & the driver will stop.If you want to go from say Chaweng to Bophut you should negotiate a price before you get on because the price could range from anywhere between 50 -150 baht pp depends how much the driver wants the fare.A friendly warning however, there is a bit of a songtaew mafia that operates late at night from Soi Green Mango & pray on inebriated tourists,if you use these people be prepared to pay more than if you were to walk along the road & hale one.

Metered Taxi`s well that`s just a joke because they will point blank refuse at any stage to use the meter.If you feel the need to use these negotiate a price before you enter chances are he will have a list of standard prices that they will not budge from but if your lucky the odd one will.EG a ride along beach road Chaweng is 100 baht, a trip to Bophut from Chaweng is 300 baht.

Another transport option especially in Chaweng is a motor cycle taxi I think it is 10 baht along Beach road you can spot these men easily as they will have a vest on with taxi & a number on it.This is a cheap faster way to travel along Beach road especially if your by yourself.

However the best part of Samui is your own Scooter which costs 150 bhatts per day + Petrol ( 40 bht in Chaweng, 35 around the island suburbs, 30 bhatts in petrol pumps). If you hire a Scooter in Chaweng it might cost more but at the same time you will have the inconvenience of returning it. Bet bet is to hire the scooter nearest to the place you are staying. They might ask for a Passport deposit but you can try to negotiate to another document say your outward ticket, ID Card, License.

 Exploring the town with the abundant maps available in your scooter gives you the freedom of movement without bothering about the costs. A whole round trip of the island with its scenic environment with the help of the map will take not more than 2.5 hours.

 Another option is to take theSelf Driven Car which can be available at 1000 bhats if you are a family of 4.