You can reach Thyon by car, taxi or bus (3 times a day) from the nearby town of Sion, or by bus (8 times a day) and cable-car (runs from 9am to 4pm) from Sion via Veysonnaz. Timetables available from the Swiss Federal Railways.
Sion is easily reachable by car, bus or train from either Geneva, Milano or Zürich. As you can see on the following map, the bus station to Thyon (or Veysonnaz) is right next to the main Sion train station.
is the closest airport and is a big Easyjet hub, providing lots of opportunities for cheap flights. This is the cheapest and fastest train service to Sion (1h40), and as an added bonus, the train leaves directly from the airport.
A return ticket is about 120 CHF, but you can get big discounts (up to 50%) if you book a Supersaver Ticket 30 days in advance on the website of the Swiss Federal Railways.
is the next best alternative (either airports). The Freccia Rossa (red arrow) high-speed train will take you directly from Milano Centrale through the Simplon tunnel to Sion in 2h40. Make sure to get a ticket in advance, as the trains are often completely booked!
is another good option, just 2h30 away from Sion, but you will have to change train at least once (in Lausanne or Visp).