I will go ahead and admit that this is not going to apply to a great many people out there but if I had this information before I tried to go and get mine I would have been happy to know it. It took me a week to figure this out and I can speak Thai. Put a non Thai-speaker in this situation and it will take much, much longer
I'm gonna go ahead and say that I find it bizarre that someone that is not from this country can be issued a driving license by this country - but it is possible. The requirements are not terribly difficult and the test you have to pass is absurdly easy. That being said, if you are just passing through, you do not qualify for a Thai driving license.
So here are the things you need in order to acquire a Thai driving license
your visa needs to be a Non-Immigrant B (business) ED (education) or Non-Immigrant O (normally because you are married to a Thai person but their are other reasons) visa.
you must have a medical clearance certificate from a doctor - this normally incorporates talking to a receptionist and paying them 100B to write your name and passport number on a document. Seriously, it is dumb and I can't imagine why this is still part of the verification process because i have been through this many times and have only ever had an actual doctor look at me once.
You need to have a real address ( I know, details, right?) this is done via house papers and the id card of the owner, and you take these papers to the Immigration office who pretends to know where that house is and then makes you another piece of paper falsely claiming that the address is verified.
You need to submit a copy of your lease. Most leases are made on MS Word so yeah, there is no official form. It would probably be helpful if the lease is in Thai to add more credibility to it. The best thing to do would be that the lease is actually legitimate (I am not encouraging anyone to break the law.)
you pay a relatively small amount of money like $40 or so
you watch some poorly produced videos that aren't even in English but are required anyway
you sit for a test where most of the questions have been poorly translated into English and don't make sense including multiple questions that have options involving military tanks. Don't worry - you are not allowed to fail. If you do fail, you will just be asked to take the test until you don't. IF it takes too many times to pass the instructor will eventually just tell you the answers
You will have to do a field test which incorporates such complicated anomalies as starting the car and turning it off, backing into a parking spot, dodging orange cones that are ludicrously far away from one another, and parallel parking into a spot that a B-52 bomber could fit into.
After all of that, you shake your kind instructor's hand and wait a few days, pay about $40 more and now you have a provisional Thai driving license which is valid for 1 year.
I found it to be lots of fun when i returned to the United States and needed to rent a car but did not have a US driving license. I did have a US passport and a Thai driving license. It took multiple phone calls to the "home office" to determine whether or not they were going to let me rent the car. They did in the end and I crashed the car almost not at all (I didn't crash the car.)
So there you have it folks. It may not occur to you while you are visiting Thailand to get your internationally recognized driving license (it't not really recognized internationally,) but now you know that it is an option should you feel so inclined to get one while you are here. By the way, the police generally speaking aren't terribly fussy about whether or not you have a license from any country when driving here, let alone one from Thailand.