With the expressway from Lausanne - Sion - Sierre - Brig - Ernen - Binn.
Via the Lötschberg tunnel with the car train:
Coming from Bern you drive to Kandersteg and there you board the car train "Lötschberg" to Goppenstein. From there you head toward Gampel and then to Brig and further onto Ernen - Binn.
Via the Furka tunnel with the car train "Matterhorn Gotthard Bahn" or in summer you can cross the Furkapass:
From East and Central Switzerland drive in the direction Göschenen - Andermatt - Realp (here you can board the car train) "Matterhorn Gotthard Bahn" - Oberwald - Fiesch - Ernene - Binn.
Passes that are open in the summer:
Grimsel pass (northern connection)
Nufenen pass (southern connection)
Furka pass (Eastern connection)
Simplon pass is open all year round
Car train "Matterhorn Gotthard Bahn" Furka: Realp - Oberwald, approx. Every 60 min.
Car train "Lötschberg" Lötschberg: Kandersteg - Goppenstein, approx. Every 30 min.
By Train
From Geneva/Lausanne with the Schweizerischen Bundesbahnen "SBB" to Brig and from there with the "Matterhorn Gotthard Bahn" to Fiesch.
From the directions Basel/Zurich/ Bern take the Bern-Lötschberg-Simplon-Bahn "BLS" to Brig and from there with the "Matterhorn Gotthard Bahn" to Fiesch.
From East and Central Switzerland take the "SBB" to Andermatt and then with the "Matterhorn Gotthard Bahn" to Fiesch.
You can reach Binn with the local bus (Ortsbus), which departs from the Fiesch train station.