Transport from zurich airport to murren

Trains are the best option. Consider one of the various train passes ( Jungfrau, Berner Oberland, Swiss travel Pass) to save money.
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take the train.

All the connections along the way knit together beautifully and are very easy to do. Much faster than any other method.

Train from the airport to Bern, change there for the train to Interlaken Ost, change there for the train to Lauterbrunnen. Cross the road and take the cable car to Grütschalp and change there for the train to Mürren MLB. Walk out of the station and you're there.

Sounds complicated, it is easy

Consider one of the various train passes ( Jungfrau, Berner Oberland, Swiss travel Pass) to save money.

Or the Half Fare Travel card. It all depends on what your travel plans in Switzerland are. How long you will be there, where else you are going? If this is more than a month or so away, also the Saver Day Pass.

Also, if you time it right, there is a train that you won't have to do any transfers on until you get to Interlaken Ost. This makes things SO much easier. the 14:45 and the 16:45 trains. the 14:45 train might be super tight unless you can be really efficient getting off the plane, getting your bags and going to customs, but it IS doable. Otherwise, lounge around the airport, get something at the Migros to eat on the train and then make your way to the station just under the airport and hop on and go.

trains from airport to Lauterbrunnen

We were just there few days ago. Like previous post states, it seems little complicated but it's not. Once you are at Interlaken OST station, take Lauterbrunnen train and then Grutschalp cable car (Signs clearly display the direction from platform), it only takes 4 minutes and then you hop on another short train ride with amazing views to reach heavenly Murren.

If you can, time it for the direct train to Interlaken Ost to save one extra transfer. If not, is what it is. Then train to Lauterbrunnen, cable car to Grutschalp, train to Mürren. It’s a car free village so there is no getting around having to use public transportation. You should pack efficiently and as lightly as possible because of this. No one cares what you’re wearing in this area, so no need to pack extra for fashion.

The connection in Interlaken is always short, so be prepared to hustle with your luggage down the ramp and back up and make sure to go to 2A, not 2B. The train splits in transit and the back half goes to Grindelwald, so you must be on the 2A section labeled Lauterbrunnen.

And don't be upset if you miss a connection. There will be another train in 30 minutes.

Thanks to all responders to my query re transport Zurich to Murren!