Budget Travel - When to buy ticket?

Hey All,
I'm going to be in Thailand from around the 10th of December to the 3rd week of March.
I've never bought an airline ticket before.
Should I buy a ticket well in advance, or wait until around December 10 for last minute deals?

Any suggestions on where I can get the cheapest ticket? I'm travelling from the U.S., and budget is a very important consideration.

Thanks,
Nickto