There are mini-buses that leave from Khanom every hour from about 06:00 until 16:00 to Surat Thani and Nakhon Si Thammarat. There is also big bus and a VIP bus that goes to Bangkok every day at 17:30. It arrives in Bangkok about 12 hours later.
Khanom is between 2 bigger cities and about 20 mins away from Donsak Ferry pier, which has ferries to Ko Samui and Ko Pha Ngan.