These days you can get international flights into several key cities in Thailand including Bangkok, Chiang Mai, and Phuket. The easiest way to find the cheapest flight is to book through a comparison site such as Vayama. Once inside the country it’s easy to get anywhere with a direct flight.
Thai Airways is the national carrier but these days every major airline flies into Thailand or has a code share with another company to do so. I fly with Emirates as they seem to have the best connections and availability linked with a reasonable price. They also fly A380s which is an added bonus.
For domestic flights within there are choices. Thai Airways offer routes but tend to be the most expensive. Lion, Nok Air, Air Asia and Thai Smile (Thai Airways low cost option) are the main low cost choices and they are close in prices. If you book early you can get one way flights from as little as 800 baht including taxes. I budget between 2,500 baht to 3,000 baht for a return flight if booking a few months ahead.
Bangkok Airways flies out of Samui but has a limited selection of international flights. Flights are expensive in comparison to other destinations. People choose to fly to nearby Surat Thani airport and take a Ferry to the island.
Operators will offer a plane + bus/boat ticket on their website for Samui and other popular islands. To give a real life example a midweek return flight, booked three months ahead to Samui costs 7,350 baht. But a flight+bus+boat ticket to Samui via Surat Thani airport costs 1,955 baht on the same dates.
For those thinking of moving to Eastern Sea Board there’s the new U-Tapo airport. They have opened but is still building up flights. I expect within a couple of years there will be more internal and international flights to this airport