Not sure I can give the best directions - a friend drove, so I didn't pay that close attention, but here's the link to the hut.
It states that you can leave from the Susten highway at Fuhren and walk to the hut in 1.5 hours or take a tram directly to the hut. If you drive, you have to get (buy) permission to drive the Birchlauistrasse.
The trail from the hut to the base of the Klettersteig is easy to find and you can always ask the hut warden. If I recall correctly, it takes about 45 minutes at most to get there from the hut. The way back which is down the other side and up and over a little pass back to the hut is long - so don't leave too late. When we did it, we actually walked down to Engstlealp, where you can catch a bus (we had someone pick us up) Parts are very exposed, so having and knowing how to correctly use Klettersteig gear is essential.
Here's the link for the Klettersteig
It's fun and the views are fantastic.