Presuppositions are beliefs that someone practicing NLP will find useful for creating changes in themselves and the world, more easily and effectively. The emphasis here should be on "useful" not whether each one could be proven to be "true". Practitioners of NLP often include different presuppositions in their list but what follows are the most common.
People already have all the resources they need to effect a change. The resources just weren't lucky enough to be in the right place at the right time.
Choice is better than no choice. Need I say more?
Every behavior serves a positive intention and a context in which it has value. The behavior may never lead to that positive intention but that part of you can learn new behaviors that do. As to a context that has value, imagine overeating at an expensive brunch (got your moneys worth didn't you?). Go with me on this one, it really helps.
There is no such thing as failure, only feedback. Every response is useful, you may hate the response but the knowledge you gain from it is valuable.
If someone can do something, then it can be modeled and taught to anyone else. That even includes me.
The map is not the territory. We cannot contain every bit of information that comes to us in the world, so we have to create a "map of the territory" and then refer to the map for our information (see representational systems). By changing a person's map, we change their reality.
The meaning of your communication is the response you get. If you get slapped, try anything else.
If you aren't getting the response you want, try something different. See above.
People work perfectly. No one is "broken". They are functioning perfectly in what they are doing now (even if it is ruining their life), it's a matter of finding how they function now, so that we can help them change into doing something they consider more desirable.