Trang is a city in southern Thailand.
South towards Satun
In direction south you will have to use the airport road, but apparently there is no public transport there and it's quite a walk. You can take a Tuk-Tuk to the Tesco supermarket on that road and then walk a little further south where the bypass merges into the airport road. This makes a good spot to hitch.
You can walk or take a bus to the bus station East of the town. Then walk about 200 m along the main road and just hitch there. It should be easy to get a ride to Patthalung where you can let your driver drop you off right at the Suratthani-Hat Yai-highway.