Around Khanom
There is no local bus service in Khanom, and very few song-taws , no tuk-tuks, but quite a few motorcyle taxis. You could rent a pickup if you like, or hire someone to drive you around. Mini-vans are also available on a half day or daily basis.
Bangkok
You can fly from Bangkok to Surat Thani, Nakhon Si Thammarat, or Koh Samui. I can arrange pickup from Nakhon or Surat, the price is around 2000 baht.
There are two or more buses leaving from the Southern Bus Terminal around 7.30. They arrive in Khanom; which is the end of the line; around 6 a.m. .
You can take the train to Surat Thani or Nakhon Si Thammarat, and then take a mini-bus to Khanom.
Hat Yai
You can take the 7.30 or 10.30 buses to Koh Samui and tell the driver you want to stop in Amphoe Khanom. The bus to Hat Yai passes by at 10.30 and 12.30.
Nakhon Si Thammarat
Mini-van, across from the CP Mart
Surat Thani
Mini-van
Don Sak (Ferry Pier for Koh Samui, etc.)
There is infrequent sang-thaew service at the pier. Motorcycle taxis are available, or I can arrange for you to be picked up by motorcycle, pick-up or mini-van.