Leysin is served by the TPC (Transportes Publics du Chablais) which has a cog-wheel train which runs once per hour from the Aigle station, which is timed to connect with the main Swiss National trains arriving from Montreux on the Geneva-Brig line. On certain dates during the ski season there are direct TGV trains from Paris to Brigoffering the same connection at Aigle. The trains up to Leysin leave from track 12, which is actually in front of the Aiglestation in the parking area (it's the track closest to the buses).
There are multiple stops within Leysin, notably Leysin-Village, Versmont and Leysin-Feydey. Leysin-Feydey (024 494 11 16) is the station closest to the TÚlÚcabines. For other destinations check the destination listing below for the correct station