I think you're fine with a PGCE or a Masters, if in Ed. Apply online at Kru sapa, the Teacher's Council of Thailand. You could also go there, show them your qualifications and ask. They'll tell you what to do.
The DLT at Chatuchak in Bangkok have a foreigner's desk. They sort out your paperwork and tell you where to go. You can do it yourself in a couple of hours if you have a license from your home country.