Summarize:

On many modern designs, this is a relatively simple process. De-cock the hammer (or striker), pull the take down tabs. After a pull toward the rear of the frame, the slide should be able to move freely off the front of the handgun. The actual process may vary greatly depending on the model of firearm you are field stripping. Glock & Steyr users: Be triple-sure your firearm is unloaded as you must pull the trigger on the firearm to initiate the field stripping process. There are four major pieces to every semi-automatic handgun (though they may be attached in different ways). Frame: this is the stock (or "grip") of the handgun. The trigger assembly is usually embedded in the frame, and the magazine well is located inside of the stock. Slide: the piece of metal on top of the firearm; it keeps the chamber sealed, compensates for recoil (on many semi-autos), and houses the firing pin (and a few other components). If you have a polymer frame, this is where 70% (or more) of the gun's weight is. Barrel: the barrel assembly is the barrel and the chamber. Be cautious with the muzzle-end of the barrel and the beginning of the rifling (inside the barrel), as these are the two most important things to affect accuracy and can easily affect it adversely, if damaged. Guide rod and recoil spring: often these are one piece. The guide rod guides the slide as it recoils and the recoil spring pulls the slide back into place after a round is fired.
Dismantle the firearm safely. Identify the parts you are cleaning.