Mürren is car-free, which means the journey in is part of the experience. From Interlaken Ost, take the train to Lauterbrunnen and then the combination of cable car and mountain railway (Bergbahn Lauterbrunnen–Mürren) up to the village — the journey takes about 45 minutes from Lauterbrunnen. Alternatively, from Stechelberg at the valley floor, a cable car (Schilthornbahn) goes directly to Mürren in about eight minutes before continuing to Birg and the Schilthorn.
Swiss Travel Passes cover the train to Lauterbrunnen and usually give discounts on the mountain railway and cable cars. Driving gets you as far as Stechelberg; there is a car park at the cable car base station.