Yes, I think the best way to start is by looking at your school's study abroad programs. I'm sure your school should have an office with people who are responsible for giving this information. Hopefully your school also has affiliation or relations with schools in Thailand, otherwise I've heard of people going abroad by enrolling through a school they aren't in right now (I'm not sure how easy that would be though). I'm assuming you're an undergrad? Good luck!
My recent (and waaay too brief) visit to Thailand made me REALLY want to study abroad there, but I too am not sure how that would work through my university, as I have the impression that there has to be a specific program set up beforehand, instead of simply requesting. But go for it anyway!!!