There are a number of ways to weather a model, it obviously depends on the type of finish, eg. dust, mud, stone chips etc. I have never weathered a slot car, but have weathered many Tamiya WW2 German Tanks and Games Workshop 40k vehicles. The method I used for these was to simply dry brush on various layers of colour. Building up the layers will give a much more 3-D appearance. Mud or dust never sticks on in one go, it builds up over time.
I would imagine the best method for a slot car would be to airbrush on a couple of lightish coats with the second coat lighter than the first. This would give the appearance of dust or mud (depending on you preference). Obviously you would only need to spray from one direction to give the appearance of the car going forward. You could flick some watered down paint from a brush, again from one direction to add water splashes etc.
Best thing is to practice on an old model, or purchase a cheap die-cast car from a car boot or something.
M