From Mount Wiki

[edit] By Bus

Busses to Brig:

• Simplon - Gondo
• Saastal
• Blatten
• Mund
• Rosswald

[edit] By train

Brig is the main city of the upper Wallis and the junction of the trains:

• Bern - Lötschberg - Simplon - Domodossola
• Furka-Oberalppass (Andermatt/Disentis, Glacierexpress (this one is expensive))
• Brig - Visp - Zermatt
• Lake Geneva - Milano