Like an airplane a hydrofoil wing generates lift as water flows around it. The longer distance on the upper part of the wing creates lower pressure which pulls the wing upwarts. The bottom of the wing will also create lift, cause the water pushes it upwards. But that is actually less than what is produced on the top of the wing.
Many different designs of wings have been used for hydrofoils. In general you can distinguish the types.
There are 3 main ways of propelling a human powered hydrofoil.
Most HPHs are driven by a pedal powered Propeller. In a bicycle like set up, either sitting or lying, the driver powers a chain connected to the propeller. The propeller is either under water or as with the decavitator above water similar to a airboat.
Recently the flyak showed that you also can use paddles to power a hydrofoil based on a kayak.
But probably the most interesting way to power a hydrofoil is by Flapping Wing Propulsion. This kind of propulsion is the only one which is unique to human powered hydrofoils. In no other machine man has been able to use one of natures most natural way of propulsion. In order to do so, the rider has to make the wing (or wings) flap the way also a bird would flap his wings or a fish uses his fin. The combination of the absolute smooth ride of a hydrofoil with the wavelike up and down motion creates a sensational riding/flying experience.