Bangkok is the arrival point for just about every visitor to Thailand. If you are travelling on from there to other Thai cities by air and have pre-booked in your home country then it will most likely be by Thai Airways. While not unreasonably priced by international standards, you can still fly for a lot less if you are prepared to collect your luggage and re-check at Bangkok Airport.
This is made possible by the emergence of several low cost airlines aimed mainly at the domestic Thai traveller. The quality of the service is quite good and the flights are amazing value whichever city you head to. For people wishing to connect with international flights, these airlines may also offer a more convenient schedule that will prevent you having to hang around Bangkok Airport any longer than necessary. However, take care to check that the connecting flight departs from the new Suvarnabhumi International airport and not the old Don Muang Aiirport which is a two hour drive away.
Advance bookings may be difficult through international travel agents but they can be made at the company websites (see links at bottom of page). If you don't want to plan your movements ahead of time then the good news is that you can usually get seats by just turning up on the day of travel though this not such a good idea in the high season or during Thai public holidays (and they have a lot of them).
For Thailand visitors on a tight budget or who maybe just have time to spare, you can travel even cheaper by using the country's road and rail transport. The rail service runs to some major towns and cities (connections by bus will be needed for beach resorts) and can be a leisurely and comfortable way to take in the sights. The overnight train to Chiang Mai is especially recommended for comfort and value. The Orient Express its not, but if 2 people are travelling you can get an air conditioned cabin with sink, powerpoints and large comfortable bunks for a very reasonable price.
If travelling at the lowest cost possible is your priority then there is no shortage of intercity buses. They can be broken down into two categories : those with, and those without air-conditioning. The aircon buses are usually modern and very reasonably priced while the non-aircon are just plain cheap but can be recommended only to the most resilient tourists.
Useful Links -
Nok Air : Thai domestic flight bookings
Air Asia : Thai domestic and International flight bookings
Orient Thai Airlines : Thai domestic flight bookings
State Railway of Thailand : rail network information and timetables