Not sure of the exact details for the F1 or the GTrs but the principle is pretty straight forward.
By controlling (reducing) the amount of air flowing under the car you increase the airflow and create suction. This helps draw the car to the floor. The ultimate in this is "ground effect". If you have bits and pieces of engine, transmission, exhasut in the way you get two disturbances. Firstly you get turbulance which, whilst it is reduced by the creation of boundary layers around the items still causes uneven flow. This creates areas of stall and can lead to an air dam at the front of the vehicle. Secondly, you get differences in temperature and this causes the air to react differently under the car at various points.
For a standard road car there is limited improvements you can make. In principle it is easy to make a minor improvement (most performance cars try to achieve something) but the likelihood of making a significant difference is limited (unless you have huge amounts of money).
By putting on a deeper spoiler at the front you reduce the airflow underneath (which helps) however this is compromised by the fact the air now has to find an alternative route over the car, through the engine bay or around the car. Every time you do this you create more turbulance. The only way to overcome this is get the car as low (in total terms) as possible.
Having done all this (or tried) you may then find you have problems with cooling. Some of the really big R34s have gearbox problems. By reducing the airflow under the car and encouraging arfolow through the engine out through the top (rather than underneath) the latest Skyline's gearbox does have a tendancy to overheat far more than the R33.
Additional work can be done at the back of the car. Having smoothed the airflow with a flat bottom you can then create high downforce by having an undertray at the rear the opens upwards - see the R34's rear undertray.
In short - keep the air underneath to a minimum, keep it flowing (as quickly as possible) smoothly to the back of the car and control its escape.