Travel

You have direct access to the front door of the Chalet, without any steps, if you access via the Steinmattschleif road. Taking an e-taxi to arrive at the Chalet is the most convenient mode of transport, given that Zermatt is a completely pedestrianized resort.

From Zurich Airport

The journey takes about 3.5 hours and the e-taxi has access to the front door of the Chalet.
E-Taxi: http://www.3535.ch/de/allgemein/home

If you prefer travelling by public transport, the easiest way would be to take the train from the airport to Visp and then take a e-taxi from Visp to the Chalet in Zermatt. You can also take the Glacier Express from Visp to Zermatt station and take an e-taxi at the station.
Train: http://www.sbb.ch/home.html
E-Taxi: http://www.3535.ch/de/allgemein/home
Glacier Express: http://www.glacierexpress.ch/de/fahrplan_ticket/fahrplan/winter/Pages/default.aspx

From Geneva Airport

The journey takes about 4 hours and the e-taxi has access to the front door of the Chalet.
E-Taxi: http://www.3535.ch/de/allgemein/home

If you prefer travelling by public transport, the easiest way would be to take the train from the airport to Visp and then take a e-taxi from Visp to the Chalet in Zermatt. You can also take the Glacier Express from Visp to Zermatt station and take an e-taxi at the station.
Train: http://www.sbb.ch/home.html
E-Taxi: http://www.3535.ch/de/allgemein/home
Glacier Express: http://www.glacierexpress.ch/de/fahrplan_ticket/fahrplan/winter/Pages/default.aspx

From Mailand Malpensa Airport

The journey takes about 1.5 hours and the e-taxi has access to the front door of the Chalet.
E-Taxi: http://www.3535.ch/de/allgemein/home