This is a node your homework writeup. I am currently studying to be an NLP practitioner.
Update: 21/04/2007: I've now qualified as an NLP Practitioner and also as a hypnotherapist.

What is NLP?

Neuro: Our nervous system through which we gather and process information from our five senses: See (Visual), Hear (Auditory), Touch (Kinaesthetic), Smell (Olfactory), Taste (Gustatory).

Linguistic: Language and non-verbal systems through which our internal representations are coded, ordered and given meaning.

Programming: The patterns, programmes and strategies that we run in our neurology to achieve our specific and desired outcomes.

This approach is combined with an attitude of wanton curiosity, experimentation and confidence.

The methodology of NLP is to use modelling techniques, of physiology, language, filter patterns and strategies. The three original people who were modelled for the basis of NLP theory were: Virginia Satir (family therapy), Milton H. Erickson (hypnosis) and Fritz Perls (gestalt therapy).

The NLP Communication Model

                 ____________
 Meaning      ---            ----___
  ___     <====                     \
 /   \           Filters             \      /
| I R |         /       \        _   /     / ============
 \___/          |Delete  \      / \ /     /    EXTERNAL
 Focus          |Distort  \    | @ |      \    EVENT
   |            |Generalise|    \_/ \      \ ============
   |            |          |         \      \
  ___           |          |          \
 /   \          |          |           \
|State|         |Beliefs   |            |
 \___/          |Values    |         ---
   |  \         |Memories  |         \
   |   \         \________/           |
  ___   \                           _/
 /   \   \                           \
|Body |   \                           |
 \___/     \|                 ________/
         Response           /
             \             /
              \
               ->Behaviour--------->> Results

How this works is that sensory data arrives in the form of External Events. There are over two million of these external events happening all the time. However, the conscious mind is only aware of and tracking, seven plus or minus two items.

External events reach the conscious mind by passing through filters. The first of these is deletion. Think of this as a tuned circuit in a radio receiver, which picks out one radio station from the mass of noise coming in on the aerial.

The next filter is distortion; this can be analagous to another part of a radio - that which recovers the audio sound from the radio signal. In neurological terms though, what is happening is that the sensory data is adjusted into a form that fits with previous memories, beliefs and values.

The final filter is generalisation, which takes observations about specific details, and turns them into general forms, based on prior memories and other instances of similar events happening.

What has happened to our event now is that we have derived a meaning for it, which is added to our internal representation of the world. Such additions can result in large shifts (shocks) in the internal representation.

Based on the focus (the 7 ±2 items that the conscious mind is aware of), changes in internal representation can result in a change of state, resulting in a change in physiology (body language) and maybe generating a response, causing some behaviour and some results in the outside world.

NLP courses and qualifications

Beyond free events where NLP is demonstrated, are introductory workshops, like the 3 day "Fire your desire" course I attended in February, where I took part in a repatterning, which was amazing! I have sorted out some long term behaviour patterns, which were limiting my life.

To study NLP, the levels are: NLP practitioner, master practitioner, trainer and master trainer.

Here is a list of topics you would expect to be covered in NLP Practitioner:

Source

NLP Practitioner Certification Course with Andy Harrington: home study pack.