While hot-wiring a car may seem fun in the movies, it is highly illegal. Granted, there are some instances when having the skill could be handy (when you lose your keys, for instance). If you are seen doing it, you could very well be reported to the authorities. Bearing that in mind, it is a useful skill that every responsible adult should at least comprehend.
Place the car in neutral.
Find the "live" wires. Look beneath the steering wheel and find the two wires that run up the steering column into the ignition panel. There are other wires as well, but these are the only two that run up to the ignition.
Strip the insulation from the tip of the wires, being very careful not to touch the wire itself. You can seriously shock yourself if you do.
Hold the wires gingerly by the insulated part and gently touch the tips of the two bared wires together. You should see a lively little spark. Your engine may even try to turn over on the first try.
Keep doing this as long as needed, until your engine turns and the car starts up.
Discontinue touching the wires together when it starts and give the car a little gas with your foot to keep it running. If possible, try to re-cover the wires with the insulation and push them up and far away from you. Then you are ready to roll.
If you have a small screwdriver, you can try to start your car with that, simply twisting it in the ignition like you would your key. Sometimes you can get lucky, and this will work. This method will only work on older model vehicles.
Never touch the stripped wires with your fingers because you could be in for a nasty shock. When putting the wires back in place, be sure to keep them far enough away that you don't accidentally bump them with your legs. You could get badly shocked and cause an accident to boot. With newer model cars, be careful you are grabbing the right wires. Make a mistake and you could trip the air bag. Hot wiring is illegal, so be prepared to prove ownership if someone sees you doing this.