The easiest and most inexpensive airport in Thailand is the Suvarnabhumi Airport (BKK). From the airport you can take a train towards the city, or a taxi. With taxi services, you should negotiate all rates before entering the cab.
While traveling between regions of Thailand, simple flights connect most major cities with flights nearly every hour of the day between more major cities. Tickets can be bought at the airport for the next departing flight, or booked more than 24 hours in advance. Also, Thailand does have a comprehensive train system if you have the time.