It's hard to define the word permanent when it comes to hair removal. Permanent hair removal has been established as the complete destruction of a hair follicle's ability to regenerate and grow hair. It would be a wonderful thing if that meant forever.

Electrolysis
A hair-thin metal probe is slid into a hair follicle.
Proper insertion does not puncture the skin.
Electricity is delivered to the follicle through the probe, which causes localized damage to the areas that generate hairs.

Advantages: By far the best and longest track record of results
Disadvantages: Can be expensive, can be painful, can be tedious, and can be difficult for large amounts of hair. If done improperly, it can result in: partial to full re growth, lasting skin damage and/or spread of infection.  

Click Here for an Interesting Article About Hair Removal Written by Marian Segal of the FDA

Click here to read more about laser hair removal..

Friction Hair Removal: __________________
Facts: Less common method of removing hair at skin's surface, but some consumers find it useful for fine hair on legs.
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How it is done: A rough surface usually mitts, Pumice stones or emery/sandpaper is used to buff away hair at the skin's surface. The mitt usually has rough strips or a smoothing surface coated directly onto the mitt.
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Advantages: Inexpensive, fast, essentially painless, can be done at home, available widely, also exfoliates and smoothens skin. Many types can be used wet or dry. Good for legs with fine hair. Some use it between shaving or waxing sessions.
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Disadvantages:Effect lasts a short time-- anywhere from a few hours to several days. Dark-haired users may have a visible "shadow" of dark hair under skin. Often it requires use every two or three days. If rubbed to hard it may cause skin irritation. Not for use on face, arms, or bikini area. Do not use on irritated or damaged skin