Getting an international drivers license in Bangkok is relatively quick and painless. The first place most people think of is to go to the Department of Land transport located at Mo Chit, which is located right beside the Civil Aviation Training Center. The department is located right in between Mo Chit and Saphan Kwai BTS stations, and is around a ten minute from either station.
You might be able to apply for it at your local office. More recently, the Department of Land Transport near BTS Bangchak Station on Sukhumvit now also offer this service.
Before going, you will need to make sure you have the following:
Two 2-inch photos
Signed photocopy of your Thai drivers license
Signed photocopy of your passport
Signed photocopy of your Thai ID card
If you're a permanent Thai resident, you will need to also bring your House Registration.
Photo taking services and photocopying services are available at the place, but if you haven't prepared a photo it may slow you down as you need to wait for it to be developed.
If you're not Thai you will need to bring along an Affidavit of Residence which can be obtained at your embassy. In some cases, your work permit may suffice depending on the official looking after your case that day.
The place to go to is building 4 on the second floor. The number of each building is written in large Thai numbers, so look for "๔". Queue up in front of the information counter and let the official check that your documents are complete and in order. You will then be given a queue number and be redirected to another counter to wait.
Once your number is called, you will need to submit all your documents and pay the 505 baht fee. No separate application form is required, and if there is no one else there that day, you will receive the license (which is a small booket) within 5 minutes.