Probably the best way to reach Zermatt is by train, since you won't be able to drive once you get there anyway. Trains run approximately every hour to Visp and then on to Brig; at Visp you can connect to the main Swiss Railsystem with trains to Geneva (&Airport), Zurich (&Airport) and Basel. Timetables can be found on the Swiss Rail website .For foreign tourists,n the cheapest option is most likely a Swiss Transfer Ticket (purchasable only outside of Switzerland) which is valid from your point of entry to Switzerland to Zermatt and back.
Private cars can only drive as far as Täsch. The last 7 km must be travelled by train or by taxi .There is a Shuttle train every 20 minutes during the day departing from the Matterhorn Terminal Tasch, which contains 2100 covered parking spaces. You can take your luggage cart directly from your car, on to the shuttle, and on to the Zermatt train station forecourt.
If it's in line with your budget Air Zermatt will fly you in from major regional airports.
The nearest airport to Zermatt is Sion, but due to its very limited flight schedule, most tourists opt for Geneva, Zurich or Milan Malpensa airports.
It's also possible to book a airport transfer by limousine or van to get to Zermatt