Overview:

The general form of the Friedel-Crafts alkylation mechanism is as follows:

Adding an alkyl halide to the Lewis acid aluminum trichloride results in the formation of an organo-metallic complex. In this complex the carbon attached to the chlorine has a great deal of positive charge character (in fact, for practical purposes when dealing with this reaction, you can think of the partially positive charge as a carbocation).

The pi electrons in a benzene ring are mildly electrophilic, and can attack the partially positive carbon to create a non-aromatic intermediate (note that this intermediate has several resonance structures, so that it is not as unstable as it might appear). Elimination of a proton re-establishes the aromaticity of the ring, and the aluminum trichloride catalyst is regenerated along with a molecule of hydrochloric acid.

A word of caution about this reaction: because the aluminum trichloride generates what can essentially be thought of as a carbocation, rearrangments can occur to produce a more highly-substituted carbocation.

For example: Addition of 1-Chloro-2-Methylpropane to benzene with aluminum trichloride results in the rearranged product, t-butyl benzene, and not the product that you might initially expect (work out the mechanism if you cannot see how that product is attained).

An example of a Friedel-Crafts alkylation: