By train:
From Geneva / Lausanne with the Swiss Federal Railways (SBB) to Brig -TRANSFER- and with the Matterhon-Gotthard Railway (MGB) to Fiesch.
From Basel / Zurich / Berne with the Bern-Lötschberg-Simplon-Train (BLS) to Brig -TRANSFER- and with the MGB to Fiesch.
From east and central Switzerland with the SBB to Andermatt -TRANSFER- and with the MGB to Fiesch.
Actual timetable can you find here: http://fahrplan.sbb.ch/bin/query.exe/en
By car:
Over the highway from Lausanne - Sion - Sierre - Brig to Fiesch.
Car-train transport Lötschbergtunnel:
Berne - Kandersteg - Goppenstein - Gampel - Brig - Fiesch.
Car-train transport Furkatunnel:
East- and centralswitzerlanbd - Göschenen - Andermatt - Realp - Oberwald - Fiesch
During the summer you can also drive over alpine passes
Following pass roads are opend during summer:
Grimsel (north connection), Nufenen (south connection) und Furka (east connection).
The simplon pass is during summer and winter at any time opend.