This is a must see when in Lucerne. I mean MUST see, if you are debating amongst a few things, this should be top priority.
What you need to do is the Golden Round Trip, you can buy this ticket at the tourist information center connected to the train station. This will take you by boat from Lucerne (starts right by the train station) and will bring you to the base of the mountain. From here you would take the steepest cog rail car ride in the world to the top of the mountain. Once here you hike around for a couple hours with so many wonderful sights to see. Also at the top of this mountain are some military installations, which I thought were pretty cool! Once you are done, you then take a Gondola down the mountain. Half way down you get off to take the next gondola down. But before you do so, I recommend to do the longest Summer bobsled course in Switzerland. It cost around $7-$10 per person, but was well worth it, something I will never have the opportunity to do again, and the view is spectacular as you cruise at some super fun speeds. Once you are done you take a gondola the rest of the way down. From here your Golden Pass gives you buss access for the rest of the day, which you will take back into Lucerne when you are ready.
Note: There is food and lodging at the top of the mountain. Food was reasonable when compared to the rest of expensive Switzerland.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC