In Thailand cheapest flights to Bangkok, Chaing Mai, Phuket and Koh Sumui your best deals on discount flights will be on Air Asia Nok Air and 12 go. You will also some times find cheap flights on Bangkok Air. Sometimes not taking the really cheap flights will actually save you money especially if you are traveling with a lot of luggage, in which case you best bets for the cheaper overall flights will be on Thai air or Bangkok air. Air travel in Thailand is less now with the price of fuel dropping and the baht losing value to the dollar so it is a good time for travel in Thailand
Don't forget that if you have Thai airlines or United or any other of the frequent flyer programs in Star Alliance is affiliated with Thai Air and those miles can be figured at about .01 to .15 cents per mile.
With Thai air Bangkok air and Nok air the reservations are fairly straight forward and Air Asia now seems to have gotten there act together on line. A note is that if you book way in advance on Air Asia you are going to find some great deals Nok Air always seems to be the cheapest especially Bangkok to Chaing Mai and Bangkok to Phuket.

For Bangkok to Chaing Mai there is also the viable option of the overnight trains which gives you some scenery and can save you on one hotel night. I actually enjoy taking the train if I am not in a hurry just a cool way to travel as far as I am concerned and the trains in Thailand are some of the best trains in Asa when compared to trains in Vietnam or Myanmar see Asia Cheapest Travel for budget travelers tips