Take the Motorway A2 (Basel-Luzern-Gotthard) to Stans-south. From there follow the main road for 20 km to Engelberg. Engelberg is about 30 minutes from Lucerne. From Zurich you need about 1 h 15 min, and from Bern or Basel approximatly 1 h 45 min.
Parking spaces are available in Engelberg for a fee.
National and international connections (from Zurich airport connections every half hour with approx. 1h travel time) to Lucerne. Afterwards with the Zentralbahn in 43 minutes through varied landscape and gorges up to Engelberg.