There are excellent travel links to Veysonnaz, especially useful in the winter are the Snowjet flights (http://www.snowjet.co.uk) which run from Stansted direct to Sion which is 15 minutes from Veysonnaz by car.
Flights to Geneva, hire cars available for a car journey of approx 1hr 50 or a 2hr train journey from the airport to nearby Sion. Local buses or taxis available from Sion to Veysonnaz. Good network of local buses.
Flights to Milan. The car journey is approx 3.5 hours and the train journey approx 2hrs to Sion.
Rail links to Geneva from various European cities.
Use of car recommended to gain full benefit of the region.