Koh Samui is situated in the gulf of Thailand, about 650 Km South of Bangkok .
There are many ways to reach the island:

BY AIRPLANE:

The airline which serve Koh Samui, Bangkok Airways, fly directly from Bangkok to Samui several times a day.
From Singapore and Phuket to Samui twice a Day.
From Utapao ( Pattaya ) to Samui daily.
From Krabi to Samui 4 times a week ( Monday, Wednesday, Friday and Sunday )
Daily flights from Hong Kong to Koh Samui.

Thai Airways fly from Bangkok to Suratthani twice a day

Berjaya Air fly from Kuala Lumpur ( Malaysia ) to Koh Samui twice a week ( Thursday and Sunday )

Firefly offer flights from Penang ( Malaysia ) to Koh Samui every day.

Low Cost Budget Airlines Air Asia and One-Two-Go have daily flights from Bangkok to Suratthani.

Is possible to make ticket reservation directly from any of the Airlines Websites

In Suratthani airport, you can get the bus which goes to the ferry pier to Koh Samui ( 40 min ). The ferry boat take 1 and half hour to reach Koh Samui.

Thailand Low Cost Airlines

BY TRAIN:

There are daily trains leaving Bangkok in the evening and arrive Suratthani early in the morning. In Suratthani Train Station, you can get the bus which goes to the ferry pier to Koh Samui ( 20 min ). The ferry boat take 1 and half hour to reach Koh Samui.
Seatran is the most comfortable and safe transportation by sea. On Seatran website ( only Thai language ) you will find all the details how to get the boat from Suratthani Airport, Train and Bus stations.

There is also one train which is coming from Singapore, Kuala Lumpur and Penang arrive Suratthani in the evening; At that time you will not be able to catch the ferry boat until the next morning unless you take the night boat which leave Suratthani night market at 9pm and arrive Samui at 5am.
( the night boat is a small fishermen wooden boat which doesn't have seats, insted the are very narrow matrasses aligned next to each other where one should sleep all night. This is a trip for back packers. )

Join tickets Train-Boat are for sell in every travel agency around Thailand.

BY BUS:

There are many companies which provide Bus service from Bangkok to Samui. They generally leave Bangkok in the evening and arrive in Suratthani the next early morning; from there there is in connection with the Express boat by Songserm or the car ferris by Seatran and Raja Ferry which will take you to Nathon Pier in Samui.
Seatran is the most comfortable and safe transportation by sea, at Seatran website you will find all the details how to get the boat from Suratthani airport, train and bus stations.

There are also daily Buses from Phuket, Krabi and Hat Yai. They all leave in the morning and arrive in Samui in the afternoon or evening of the same day.

BY CAR: