Samui has an excellent public transport network of songthaews - basically, converted pick-up trucks with bench seats. Dozens of them circle the island on various fixed routes all day and fares start at around 20 baht for a short trip - this is paid at the end of the journey. There are no fixed stops, so flag one down anywhere and ring the bell or bang on the roof to get off. After dark, many songthaews operate as private taxis, so it's necessary to negotiate a fare before getting aboard. Expect to pay several hundred baht to travel between beaches.
Motorbike and jeep rental is readily available everywhere on the island. Expect to pay around 200 Baht per day for a bike and around 800 Baht for a car. It's worth remembering that Samui has some of the highest accident rates in the country though, and has many steep, sandy roads. Honda Dreams are the most common bikes available, though Yamaha Nouvo's are becoming more widespread.
Nouvo's cost about 50 Baht more, but are recommended because they are fully automatic and therefore much easier to ride. The local police are beginning to crack down on foreigners riding bikes without safety helmets and fining them accordingly. The 500 baht fine must be paid immediately at a nearby police station, whilst the police hold onto either your bike, driving license or passport as insurance. If a lot of people are caught at once, the process can take several hours.
Insurance does not exist in Thailand for motorbikes, so riders are liable for any danger and it's almost always the foreigner's fault. Many jeep hire 'bargains' will come without insurance and are therefore a risky proposition. Any established company such as Budget or Avis will include comprehensive insurance in the rental.
Bicycles for hire are increasingly common, though are not recommended for long trips at night for safety reasons.