A hovercraft works by doing two things at the same time - it pumps air under the craft hull to create an air cushion to lift the craft off of the surface (the lift system) and it also pushes air out of the back to make it move forward (the thrust system).
The Lift System
The air for the cushion is provided by either re-directing some of the thrust air from a single fan (known as an "integrated" hovercraft) OR by having a separate fan to provide the lift air directly. The height at which the craft hull "hovers" is fixed by the craft hull and skirt design and is usually between 150 and 400mm for personal hovercraft. The hover height ultimately defines what kind of surfaces the craft can travel over - if the surface is too "lumpy" then the hovercraft skirt loses it's seal against the surface and too much air escapes - the craft hull can then contact the surface. It takes a finite amount of time for the air to escape and the cushion to deflate therefore if the lift system can replace the lost air quickly enough, the craft can continue to hover over some quite rough surfaces.
The fans/propellers are driven by various types of engines from small two-strokes to motorbike, industrial, lawn mower and car engines on larger craft. These engines are usually used without gearboxes to reduce weight. The engine normally drives the prop or fan through a simple belt drive reduction system.
The Thrust and Steering
Thrust to move the hovercraft forward is usually provided by either a propeller or a ducted fan. Both push air out of the back of the craft to generate thrust. Some of this thrust air can be re-directed sideways using rudders or vanes mounted behind the prop or fan - controlled by a steering wheel or stick. This allows the driver to move the back end of the craft sideways to change the hull direction (often this doesn't result in the expected change in the direction of travel - see Driving a Hovercraft!). The steering is very similar to an aircraft in that large steering control movements are needed at slow speed and small movements at high speed.
There are no brakes on a hovercraft! Driving one is very similar to trying to drive a car on sheet ice! As a hovercraft is almost frictionless it can take a very long time to stop! The only real way of stopping quickly is by reducing lift power until the skirt and/or hull start to drag on the surface!