This blog gives you the information how to travel from Nakhonsithammarat Airport to Koh Samui like local people do.
When you arrive at Naknonsithammarat Airport by Air Asia or Nok Air, after you collect the baggage, you have to walk until the exit of the airport and you will see the limousine counter service that can take you to any places in the town or nearby area.
To go to Nakhonsithammarat Town, the join car will cost 100 Baht per person, but you have to wait until it is full then they will go. If you charter a car it will cost 300 Baht per car to Nakhonsithammarat Town. It takes about 15-20 minutes from Nakhonsithammarat Airport to the town.
If you want to go to Koh Samui from Nakhonsithammarat Airport, you can charter the car from Nakhonsithamarat Airport to Donsak Pier that it will cost about 1500 Baht per car, maximum for 4 people in the car (not much space for the baggage, if you have the big baggage and / or much more people, you have to charter the van from Nakhonsithammarat Airport to Donsak pier that will cost you 2500 Baht per way.)
Or if you don't want to charter any car or van, but just want to travel or be transferred like local people in Nakhonsithammarat, just read the next topic.