This topic is translated from Thai language in the blog of Khun isccy. Thank you for the pictures and information 
After 20 minutes takes form Nakhonsithammarat airport, you will arrive at Talad Yen (Fish market) in the north or Nakhonsithammarat Town on Ratchadamnoen Road. The picture above shows the opposite side of the road that we take the picture from the side of the van company.

The wall at the front of Talad Yen or the fish market, taking picture from the van company which located opposite to Talad Yen

The van standing by for the passengers.

Inside the office of the van company. The first van is at 8:00 a.m. from Talad yen and the last one (that can continue with the last ferry from Donsak pier to Koh Samui) leaves at 16:00 Hrs

The ticket counter inside the office.

When you buy the ticket, it will be the van ticket and ferry ticket of Seatran Ferry company together, 260 Baht per person. So, don't lose your ferry ticket, otherwise you have to buy the new one 130 Baht per ticket at Donsak ferry pier. (You normally can tell them to issue Raja Ferry company which also locate nearby Seatran Ferry company at Donsak Pier, but if you take Raja Ferry, it will not comfortable to find the taxi when you arrive at Koh Samui)

The company of the van name is Sichon Patthanakit Co.; Ltd Tel : +66(0)75 342 400 or mobile phone number +66(0) 84 5078643

The van leaves from Talad Yen every hours. (Sometimes have to wait if still not full, but the last one will leave at 16:00 Hrs even not have full people in the van) About 70 kilometers we will pass the intersection name "Klong Reng Intersection" that the van will turn right to Khanom District (of Nakhonsithammarat Province)

About one and half hour,we will arrive Donsak Ferry pier Seatran company

The van will drop you here.

Then you have to walk along this way to get on the ferry.

The view from the departure building at Donsak Pier

You have to walk along this walk way to get in the ferry
Inside the passenger room the Seatran Ferry
After one and half hour of traveling by the ferry from Donsak Pier, you will arrive Nathon ferry pier at Koh Samui
Then you have to walk from the pier along the walk way again to this building (about 100 meters long) or somtimes Seatran Ferry company has the pick-up truck form the pier to this building for free.
Then you can see many "Song Taew", the red public pick-up. The drivers will tell you which direction they will go. Chaweng or Lamai or Big Buddha area. If you go to Bophut or Maenam area, you have to take the one that go to Chaweng. The price from Nathon to Chaweng about 100 Baht per person. (Check again with the driver, no standard price.)

"Song Taew" (Song = 2 , Taew = row : 2 rows because in Song Taew has 2 rows of the seat) will stand by for the passenger every time of the ferry.