Roswell is served by American Eagle, the regional affiliate of American Airlines, with three daily flights to Dallas/Fort Worth and nonstop service to Los Angeles four times per week. If you fly in, you may be amazed to see some big iron including widebodies at the airport or flying near town at low altitude, but unfortunately, they aren't there for passenger service; the Roswell air park is a former Air Force base that has been used from time to time by major airlines as a training site for aircrews and to check out new aircraft.
Road access is via US 285 from north or south and US 70 or 380 from east or west. You go through a lot of emptiness getting there, particularly from the north; don't set out for the city from I-40 with a near-empty fuel tank. Limited bus service is available.