If you travel by car and wish to go to the canton of Wallis/Valais from from Andermatt, then you need to load it on a special car carriage in the village of Realp at the end of the Ursern valley. The train will take you through the Furka tunnel to Oberwald.
Prices for a normal car start at CHF 25.00 including passengers depending on the season. The journey through the tunnel takes 15 minutes.
The Glacier Express claims to be the slowest fast train in the world. It runs from St. Moritz to Zermatt taking in the best of the alps.
If you want to ride on it, you have to pay an additional charge to your ticket of CHF 30.00 (in 2007). A seat reservation is highly recommended or even compulsory. Keep in mind that a lot of tour groups use these trains and they also seem to be popular with more settled Americans and Germans. You could do the same trip on regional trains which is a bit more authentic as you will no doubt have fellow Swiss travellers in the carriage and you can still open the windows of the older trains which is better to take pictures.
You can reach Andermatt by train from three different directions by the Matterhorn-Gotthard-Railway (MGB). For instance, we took the national train SBB from Zürich to Göschenen and changed to the MGB there.
From Göschenen it’s a short ride up the Schöllenen ravine (when you come out the second tunnel be ready with your camera and rip down the window on the left side as you go up in order to take a picture of the famous devil’s bridge. You've only got a few seconds.
Further, Andermatt is connected to the Canton of Grison/Graubünden over the Oberalp pass or to the Canton of Wallis/Valais through the Furka tunnel.
In the railway station there is a left-luggage facility (you have to ring the bell). Opposite the kiosk there are free public toilets.
The alpine passes are very popular not only with car drivers but also with motorbikes. From Andermatt you have the Gotthard pass as well as the Oberalp pass. Also you can reach the Furka with its glacier. Take care while driving winding roads.