How is this done and how long should it take?
milo, The method suggested in the first reply is the one I prefer. From Interlaken Ost, you'll take the local Berner Oberland train to Lauterbrunnen (about 20 minutes from what I recall). When you arrive in Lauterbrunnen, walk across the street and board the Post Bus (can't miss it, it's bright yellow). That will take you to the base of the Schilthornbahn in Stechelberg (about another 20-minutes). Walk up the steps and board the Cable Car. From there, as described in the first reply. Be sure to have your Camera ready as the first segment is rather steep and spectacular! If you buy a ticket to Mürren at Interlaken Ost, it will include all modes of transport (rail, Bus, Cable Car). Happy travels!
Did this a few years back: Train from Interlaken Ost to Lauterbrunnen. Then, bus to Stechelberg. Then, catch cable car to Gimmelwald. Switch to another cable car to Mürren. The entire trip is extremely scenic and takes about an hour total. Check Rick's guidebook...I think he covers this in detail.
Head over to the Swiss Rail site: http://rail.ch It will give you a complete breakdown on how to reach Murren.