What is a hydroplane and how do they work?

By definition a boat with two or more planning surfaces. In modern hydroplanes these are of the "three point" design with sponsons that protrude from the sides of the hulls at the front, on which the boat rides and the propeller that pushes the back of the boat from the water. This being the 3 points, 2 sponsons and the propeller.
The air rushing under the boat help to support it at speed and compared to "normal boats" these is very little drag resistance offered allowing the highest possible speeds to be obtained.
Hydroplanes use the principle of 'ground force"
Some hydroplanes even have the centre section designed just like an aircraft wing to help them glide thru the air and only barely in touch with the water.

You may have noticed in an aircraft taking off, they rise from the tarmac and once in the sir tend to level off before rising again. This is the ground force effect. In simple terms it is the air compressing against the ground rather than just spilling out of the way and this provides extra lift. I am not an engineer and this may sound too technical or not well explained, just think of it as "magic"

What parts make up a hydroplane?
Firstly the sponsons.
The design of the sponson is very important, while only the very lower part touches the water at speed, the sides will help determine the corning capabilities
.In this photo you can clearly see the general shape of the boat, although the sponsons are not actually touching the water.

Front canard wing.
Most GP class hydroplanes have a front wing between the sponsons. This is adjustable at various parts of the course. Down the chutes they are trimmed fairly neutral, setting up for the corners the wing is trimmed down to push the sponsons into the water so that the boat will corner faster and better.

In these two images notice on the left the cannard wing is trimed neutral, and on the right trimmed down just setting up for a corner