Samui is an island located about 80 kilometers from Suratthani, the nearest mainland city. You can fly here with Bangkok Airways directly from Bangkok. They also have direct flights from Phuket, Krabi and Singapore. Pelangi Airlines now offers 2 charter flights per week direct from Kuala Lumpur, with availability subject to demand.
Those on a budget can take the trains from any of the above cities for as little as 1/10 the cost of flying. Many people book sleeping berths in the overnight trains from Bangkok. You will disembark at Suratthani station very early in the morning, from where you are taken by bus to the ferry for the 1 to 2 hour crossing from the mainland.