I'm trying to build a hovercraft of sorts, and I thought I'd take advantage of the ground effect. I've done some searches, but I can't seem to find any guides on the actual physics. How do I go about calculating the additional lift my hovercraft will receive from the ground effect?
Hovercraft lift is a totally different dynamics then the airplane lift. Hovercraft basically rides on a cushion of high pressure air trapped in a skirt.
Ground effect is due to the earth constraining free flow of air stream aft the wing, forcing it to build up extra pressure and extra resistance, and hence providing extra lift.
Basically you would need to fly your Hovercraft much faster like the range of 80kt, and then design its aerodynamics like a flying saucer or a teardrop shape, and test it in a wind tunnel.
It may be possible to come up with a low altitude hybrid flying a few inches above ground. But at those speeds it would need a flat runway or smooth surface of a lake. It can not possibly navigate the bumps and natural obstacles as hovercraft can.
Assuming you mean a wing-in-ground-effect vehicle, which is in flight during its cruise phase, the ground effect is relatively easy to calculate, at least for potential flows.
The boundary condition imposed on potential airflow by the ground is zero transversal flow, which can be recreated by using an imaginary wing flipped around the ground line respective to the one you are calculating. In other words, if your problem wing flies 10m above the ground, you can simulate the ground contribution by calculating the lift of that wing combined with another flying 10m under the ground and inverted around the ground axis: