Samui Airport is in the north east of the island, only around 5km from Chaweng Beach. From here you have a choice of public or private taxis or transfer by minibus.
Taxis are also a good way to travel during your stay, although you need to bargain a price before getting in, as they rarely have meters.
Alternatively you can hire a motorbike or scooter, but be warned, if you’re a first timer, Koh Samui’s not the best place to start to learn, as the area has poor roads and a high rate of accidents.