First off, please make sure that if you do this, you take a Thai speaker with you. This is not only to help guide you through the bureaucracy, it's also to show you where the damn'd place is, as the only street signs are all in Thai. However, if you are driving from Hua Hin, it is down the side road beside Pranburi Police Station, which is between Camp Tannarat and the town, about 15km or more from the edge of Hua Hin.
Anyway, once you reach the office, you will have to submit the sheaf of papers you should have prepared beforehand, including the proof of residency that you got from the police or immigration -- or embassy, if you felt like a quick trip to Bangkok! (For more info on this, check here.) You hand these in when asked and then, after a suitable wait, you have to go upstairs and have your eyesight and reactions tested. In our case, the tester was a 'gatoy' or ladyboy, which was a little different to dealing with licence centres elsewhere.
Once these tests are completed (and the value of such tests is shown by the splendid (?) level of skill on Thailand's roads), you go downstairs and wait. Eventually, you will be given a remarkably flimsy piece of card -- that's your licence! I recommend you take it straight to the nearest photographic shop, like one of the Kodak supermarkets in Hua Hin, and have it laminated, or it may not even last the year. Year? Yes, your first Thai licence is valid for just 1 year. You then go back to Pranburi and, if the gods are smiling on you, get a 5-year one. Good luck, and remember -- if you can see even a tiny patch of road between you and the car in front, some Thai in a huge pick-up will try to overtake and fill that space!