The nicotine patch is one of the oldest, and certainly best-known, medical aids to quitting smoking. Patches are placed on the skin, and work by releasing a slow and steady supply of nicotine into the bloodstream. The idea is that the patch helps wean your body off nicotine - instead of nicotine being immediately absent from your system when you quit smoking, it is gradually reduced.
The way the patch works is to break your body's desire for nicotine "spikes." When you smoke a cigarette, your body receives an immidiete spike in its nicotine levels. As the level of nicotine slowly dissipates after the spike, it will eventually drop to a point where you desire to have it "topped up" again - the need for another cigarette. If you picture a graph of your body's nicotine levels when you smoke, you would see a steady series of peaks and valleys - the peaks corresponding to the spike in nicotine levels when you smoke a cigarette. A graph of your nicotine levels when wearing the patch, on the other hand, would show a steady line: the line wouldn't be as high as your peaks, but it wouldn't be as low as your valleys either. The idea is that the patch goes for the middle ground, and your body slowly adjusts to not having spikes in its nicotine levels.
As you become more and more used to lower levels of nicotine in your system, you can reduce the dosage of the patches you wear, until eventually your body is nicotine free. Another good thing about the patch is that it is an extremely strong deterrent against smoking: if you smoke while you're on the patch, your levels of nicotine will become too high and you could suffer from a nicotine overdose, which can result in sickness and even death.
The patch is a very effective stop smoking aid. It does, however, have some disadvantages: it is fairly expensive, and at the early stages of quitting it can often cost more than cigarettes did. The patch can also cause problems with sleeping if you wear it to bed - and at the same time if you don't you will wake up with no nicotine in your system, and feel pretty bad until you put on a morning patch and it starts working. Despite these drawbacks, the patch remains the medical aid of choice for people dealing with serious nicotine addictions.