Khon Kaen's airport was raised to international standards in 2005 with the opening of a new terminal. Thai Airways has 3 daily flights to/from Bangkok that takes approx 55 minutes.
When you land at the airport you can buy a 50 baht ticket for the Airport Limo that will take you to whichever hotel you are staying at in Khon Kaen City. Purchase your ticket before you claim your baggage. When you leave Khon Kaen you can buy a 150 baht ticket to the airport. You will be picked up from most hotels and resorts in the city. There is a Hotel Limo service to and from the airport that leave from these hotels: Charoen Thani Princess Hotel, Kosa Hotel and the Hotel Sofitel.