Coming from Basel and Zürich: in Bern, take the Thun (Thoune)/Interlaken highway. In Spiez, follow the directions to Kandersteg. In Kandersteg, load the car on the train (service every 30 minutes between 05:10 am and 24:00 pm (on Sat and Sun more often), cost: 25.- (see also the site of BLS). In 15 min, you arrive in Goppenstein, where starts the descent into the valley. In Gampel, follow the road towards Sierre. Shortly before Sierre, take the left fork to Val d’Anniviers. Follow this winding road (with a superb view over the Rhone Valley) up to Vissoie, then follow the Zinal signs. (Berne-Zinal, in normal conditions, approx. 2 1/2 hours).
Another possibility is to take the Bern/Freiburg highway. In Vevey, follow the direction to Sion/Simplon. The highway ends when it exists Sierre. Shortly after the roundabout, turn right in the direction of Val d'Anniviers. This route is about 100 km longer than the one through Kandersteg (Bern - Zinal, in normal conditions, approx. 2 3/4 h).