You should leave Bangkok on Highway 3, the Bang Na-Trad Highway.
Choose the elevated road it is a toll motorway but is much quicker and safer, as there are less cars than the bottom road and the elevated road is in a much better state of repair..
Follow the signs for Chonburi and then the Pattaya & Rayong bypass.
Turn off on to Highway 344 and follow the signs to Klaeng where you should turn left at the crossroads on to Highway 3, then continue towards Trat.
About 20 Km's before Trat you should turn right on to the 3156 road and follow the road to Aow Thammachat.
Leave Pattaya on Highway 36 towards Rayong and then join Highway 3 to Trat. About 20 Km's before Trat you should turn right on to the 3156 road and follow the road to Aow Thammachat.