How ground effect works on Formula 1 Cars
Ground effect is describes a particular aerodynamic effect that causes a car to get sucked to the ground, giving it phenomenal amounts of grip. The higher the speed the greater the grip. The goal of ground effect design it to help air under the car escape, to thin the air as much as possible. The basic explanations (car diagram below should help) as to how this is done is the underbody is shaped in a way that causes air at the back of the car to exit at a greater speed than air that's towards the front (often using Venturi tunnels, see picture of Porsche 962 below) by using venturi tunnels feed the air into the low pressure zone (a vaccum/blackhole like effect) in the wake of the car (air displaced by the cars motion, see image of bottle below), decreasing the air pressure underneath and pulling the car to the ground.
Can ground effect devices be put to use on a production car (for hillclimbs etc.)?
"To be honest, there was no such thing as cornering technique in the ground effect era. "Cornering" was a euphemism for rape practised on the driver. . . When you came into a corner you had to hit the accelerator as hard as you possibly could, build up speed as quickly as possible and, when things became unstuck, bite the bullet and give it even more. In a ground effect car, reaching the limit was synonymous with spinning out."
Ground effects arent traditionally used on production cars for the same reason that large aerodynamic wings arnt used on production cars (or even rally cars), because production cars are designed to be fuel efficient and downforce decreases highway fuel economy. Ground effects don't increase air resistance like wings do but they would cause increased tire friction. Ground effect is really only useful when the ride height is low and the suspension is very stiff to keep the downforce from changing when the car pitches.
One could add a lip spoiler/splitter, a diffuser (which has other highly beneficial effects), and/or install a flat undertray so that there is less drag and receive benefits. But as I said before, aerodynamics have little use in a car with a soft suspension other than to negate lift. Anything that makes the low pressure zone behind the car higher in the back (a wing for example) will increase ground effect. If the space between the body and the wing is too great it wont create ground effect.
A setup for a car with ground effects would include extremely stiff springs, reinforced suspension, and very little wheel camber because of the decreased suspension movement (about .8-2 degrees(negative) in front and .4-1.2 in back)
Many production cars have diffusers which help produce a little ground effect, they can be made easily but the bumper often makes it difficult to find space to put one.
Here is some cheap CFD software. I'm not sure if this qualifies as "good enough" to test ground effects, but it's worth messing around with if you're curious.
How the underside's shape creates ground effect
The undersides of F1 cars during the ground effect era were designed so that bottom of the car sloped up near the back. This sloping back area is known as a "Venturi tunnel" (because of the particular shape that utilizes the Venturi effect, see picture of Porsche 962 above) The area where the car is pulled down the most is right before the underbody starts sloping upward towards the back of a car. As the air moves towards the back of the car all of a sudden there is more space than there is air to fill that space. This causes a low pressure zone (a vaccum) at the back which "pulls" the air out from under the lower, non sloped part of the car. This pulling "stretches" the air thin and draws the air out of the bottom of the car and sucks it to the road.
How a front spoiler/sideskirts creates ground effect
Heres an example I think will help. Imagine that an opened water bottle in outer space, sideways, but not moving at all. The water will remain in the bottle because there is no force acting on it for it to leave the bottle. Now consider what would happen if it were moving, or if there were a fan blowing on the right side of it, its the same aerodynamic effect (see image above). The first thing to note is that the bottle will create a wake behind, the air will be mostly still in the wake. This wake is an area of low air pressure. If the fan were powerful enough, and the bottle strong enough the water could be sucked out of the bottle by the wake.
The side skirts, the bottom of the car, and the road are (roughly) like the walls of the bottle. The back of the car is (roughly) like the mouth of the bottle.