I switched from AIS to DTAC in 2008, quite a few years ago now and I've been on the same post-paid contract (and still have the same number) ever since. At the time all I needed was my passport and address if I remember correctly. Initially they give you a very small monthly credit limit, but I now have a 10,000 Baht limit and I think they'd give me more if I asked for it. As an aside, number porting has been available in Thailand for a few years now i.e. you don't have to give up your number when you switch providers.
I believe it is pretty simple with DTAC too. I recently registered my DTAC prepaid SIM. They just took a photo of my passport details, did something on my phone and on a laptop, and it was finished. I got an SMS saying I was registered. Deadline for registration is end of July.