I think it would be really useful to have my iPhone on me while I travel just to be able to use the maps, look things up, and get in touch with people. I'm on AT&T. Will my iPhone work there? How much will it cost? I've never traveled internationally before, so I don't know these things!
Technically, you could use your AT&T plan with your iPhone in Thailand, but if you use your iPhone every day for calls and data with your current, be prepared to come home to a $2000+ phone bill (no exaggeration!). Even if you've made prior arrangements with AT&T to use your phone for a discounted rate overseas for a fee, the cost to make a phone call and use data is still very, very expensive.
The best solution to this problem? Unlock your iPhone and use a Thai SIM card when you're in Thailand. Right now, your iPhone is locked to the AT&T network, so you would need to unlock it to be able to use it on any network. AT&T wouldn't unlock an iPhone that's currently on their network, but if you have an old iPhone that used to be on their network, they will unlock it for you. Otherwise, you can pay to have someone unlock your current iPhone for you, either here or in Thailand (it's not legal, but it's definitely possible).
Find an independent cellphone accessories retailer around you and they should be able to steer you in the right direction to get your phone unlock. If you're doing it in Thailand, you can likely find a street vendor or someone at a mall kiosk who could do it for you, just be on the lookout for places that have cellphone accessories as they would be the ones who know. To unlock your phone in the States, it's about $50 USD, in Thailand, it's about $10. By the way, just to clear things up, unlocking your iPhone is not the same as jailbreaking your iPhone, you only need to unlock your phone to use it on other networks.
Once you have your unlocked iPhone in Thailand, you can go to any cellphone store and buy a SIM card and just swap it out with your current one (make sure to put the latter in a safe place because you'll need it when you get home!). These stores will be very apparent and all over the place, like the equivalent of a Thai AT&T or Verizon. You'll see storefronts and kiosks as you walk in malls and on the street and you can even find them at the airport.
It sounds like you want to make calls and use data, so tell them that. When I was there in the summer of 2012, I paid less than $50 USD to have unlimited local calls and data for 30 days, which, to me, was a deal.