The hike to Rugghubelhütte can begin either in Engelberg, or as described here, at the top of the Brunni (or Ristis) cable car. It just depends how much elevation you want to hike. From the top of Brunni, the trail meanders along the mountainside for a while before starting to climb more sharply. The views of Engelberg below are spectacular. You'll be able to see the hut above you from a ways off as you approach. At the hut, enjoy lunch and a beverage -- or stay the night! You can book at https://www.rugghubel.ch/.
From the hut, you can return the way to you came or continue on towards Rot Grätli (which I highly recommend). It's more elevation gain, but the landscape beyond the hut and up towards the pass is beautiful and unique.