How exactly do you get to the top of the Arch in St. Louis? Is it some kind of conveyor belt, stairs or an elevator that goes sideways in an arching manner? I just cannot picture this.

By a tram, passengers in groups of five enter an egg-shaped compartment containing five seats and a flat floor. Because of the car shape, the compartments have sloped ceilings low enough to force taller riders to lean forward while seated (for this reason it's recommended that the tallest of the five passengers in the car sit in the center seat facing the door). Eight compartments are linked to form a train, meaning that both trains have a capacity of 40, and that 80 people can be transported at one time. These compartments individually retain an appropriate level by periodically rotating every 5 degrees, which allows them to maintain the correct orientation while the entire train follows curved tracks up one leg of the arch. The trip to the top of the Arch takes four minutes, and the trip down takes three minutes. The car doors have narrow windows, allowing passengers to see the interior stairways and structure of the Arch during the trip.

I've lived in St. Louis most of my life, and I've been up in the Arch many times. You are seated in trams that go up the Arch at an angle...like an elevator in a way but it feels more like going slowly up the first high slope on a roller coster. It's doesn't take long at all. But, if you're phobic about tight spaces, I wouldn't suggest it.
I found a few videos on YouTube that people took from inside one of the tram cars...

it looks like an egg, and you sit in it and it takes you up to the top. its really not that mind boggling.

I don't know about all that egg business, but I heard that they put you in a cannon and shoot you up the inside wall. There is a pad at the top that catches you.
It's a water slide to the bottom.

Um, I don't think there is a way that people can get up there on the top unless they climb or get a jetpack if one exsist now days.