There are two bus stations in Bangkok: nothern (Mo Chit) and southern (Sai Tai Mai). Buses to Koh Samui depart from both stations. International flights from Europe arrive at the Suvarnabhumi airport. The nearest bus station is Mo Chit. There is no direct bus route to the bus station. Bus schedule and prices can be found www.sawadee.com/thailand/transfer/bus-samui.html">here.

The easiest way to reach bus station is grab a taxi (400-600 baht). It will be cheaper if you go by bus.

The first option (from Suvarnabhumi airport):
– Bus shuttle to Don Muang airport
Bus stop is at the 2nd floor of the terminal (gate 3). The schedule — from 05.00 till 24.00 every 30 minutes, from 08:12 till 11:00 and from 16:12 till 19:00 every 12 minutes.
– Afterwards bus A1 to BTS Mo Chit station and bus terminal Mo Chit. Bus stop is at the 1st floor of the terminal 1 (gate 6), the 1st floor of the terminal 2 (gate 12). The schedule – from 07.00 till 23.00, every 12 minutes. Price of ticket – 30 baht.

The second option (from Suvarnabhumi airport):
Train to Bangkok (the lower level of the airport), follow the directions “Bangkok Airport Rail Link”, get off the the last station. Take the “Sky train” (BTS) at the station BTS Phaya Thai (walk down the corridor) and go by train till Mo Chit station (the last one). Then go by bus only a few stops.

Other options.

Train  + ferry
Train sets off from Hua Lampong  MRT station. Price of a ticket ~240 baht for a seat, ~500 baht for a sleeper coach with a fan. Then take a city bus to Seatran ferry station at Surat Thani town (bus stop is near the train station, be quick, the bus makes a short stop) and a joined ticket from here to Koh Samui. You should ask to stop near Seatran ferry office. Usually the tourists are advised to get off near the ticket agencies, the price at these companies is much higher. The price at Seatran office (minibus + ferry) is 250 baht.

By plane
There are two options. First is direct flight from Suvarnabhumi airport to Koh Samui with Bangkok Air. The tickets usually are expensive but sometimes can get good promotion price on web site.

The other option is much cheaper. From Don Muang airport to Surat Thani airport by Air Asia (ticket price is 700 – 2,000 baht), then a joined ticket bus +  ferry to Koh Samui. You do not need to buy tickets in advance, you always can buy them at the airport hall. The price is 450 baht.

Lomprayah catamaran
Bus + Lomprayah ferry from Chumpon (you can buy tickets on web site lomprayah.com). Departure from Khaosan Road (bus A4 from Don Muang airport). This is an interesting sight seen route because you will sail from Chumpon with stops at Koh Tao and Koh Phangan. It’s a favorite route of backpackers all over the world.

Advice
Do not buy a ticket for the bus + Songserm ferry. Agencies offer this route very often but it is very tiring and long, you will change transport in Surat Thani and wait for the bus at about 3-4 hours.

Moving around Koh Samui.
When you arrive in port/airport, the easiest way to get to the hotel is to take a taxi. The price from the airport to Maenam is 300 baht, to Lipa Noi – 700 baht. The price from port Raja and Seatran – is 600-700 baht (in the evening and early morning is more expensive) to Lamai and Chaweng. You do not need to book a taxi. The price is fixed.

You can also go by Songteo (red open vehicle) from the ports (100 baht) and by minibus (200 baht).