Set up your F1 car V2: Tyres, Suspensions, Aerodynamcs

Tyres - Tyres are larger on an F1 car than on a standard car and have no tread. The reason for them being slick is to maximise the surface area of the tyre and, therefore, prevent overheating. Of course, when it rains there would be no grip, since the tyres would be running on a cushion of water. Wet tyres therefore have a deep tread to disperse the water. The requirement of the tyres is to provide a contact patch between the car and the road. This contact patch must be as large as possible. The engineers can alter the size of this contact patch by altering the tyre pressure. A modern Formula One car's tyres are run at around 100oC for optimum grip. Any higher, and the tyre is being worked too hard: any less, and the full grip potential of the tyre is not being used. If the contact patch is ideally sized, then the three measurements should be fairly equal. If the central temperature is too high, the centre of the tyre is working too hard and needs to be deflated slightly. If the extremities of the tyre are too high, the tyre needs to be inflated slightly. The front tyres usually operate at a pressure of 23-24 psi and the rears at a pressure of 19-20 psi. If one side of the tyre is working harder than the other, then the angle of the tyre can also be adjusted. This phenomenon is due to the tyres being pressed into the ground whilst being driven. The contact patch of the tyre alters as all the other aspects of the car are adjusted and, consequently, the tyres are often one of the last parameters to be adjusted. (info from atlasF1 site)

Suspension - The most important elements of an F1 car suspension are the pushrods. The pushrods are the diagonal bars that link the car's chassis to the wheels.(more...)

Suspension influences  the power of the engine, the downforce created by the wings and aerodynamic pack and the grip of the tyres, and allows them all to be combined effectively and translated into a fast on-track package.

Aerodynamics - The most important  difference between a standard road car and a Formula One car is the large wings at the front and the back. These are shaped in a similar way to airplane wings, but inverted to generate downforce rather than uplift. As the angle of these is increased, the downforce increases. This is fine, but for one problem - drag. In fact, a Formula One car's drag coefficient (a measure of a car's effectiveness at reducing drag, the higher the value the less effective) is usually around 1.0 - your standard road car probably has a value around 0.3. This drag effect limits a car’s top speed. At tracks with long straights, where time can be gained by having a faster top speed, the wing angle is minimised. This results in less downforce - a problem when it comes to cornering. The compromise is hard to find for a driver, but see how the wing angle varies massively on a car between a tracks with very different natures such as Hockenheim and Monaco. There also must be a balance between the front and back wings to prevent oversteer and understeer. Sorting out the difference between aerodynamic and suspension handling is the often mark of a great driver(edit from atlasF1 site).
Example for how aerodynamics works on a F1 car explained by Martin Brundle: