Which video?

The one I linked to in the grandparent comment, which shows Brown confusing a woman about her car color.

I did not realize that NLP was involved in that trick

If you mean the paper-as-money one, that one is probably more accurately classified as a hypnosis trick using "quotes" to mask an embedded command ("it's good, take it"), although there are NLP books that explain/teach the same process. (You could consider it a form of applied priming, discovered by hypnotists and NLP people long before the modern studies of priming.)

I know little about it past the name (suggested remedy?).

Do you want technical/theoretical knowledge or practical applications? There are zillions of practical application books, most of which contain considerable amounts of nonsense.

Bandler and Grinder's books also contain lots of nonsense, but it's far more useful nonsense. (I think one even began by saying, "we're going to tell you lots of lies. None of them are true, but most of them are useful. And if you pretend to believe these lies, and act as if they're true, then your clients will also pretend to change. And if you pretend really well, they will continue to pretend to be better, for the rest of their lives.")

Anywho, Structure of Magic I and NLP Volume I are probably the best books for getting the fundamental ideas/theories, and Using Your Brain For A Change contains the basics of the technique Derren Brown used in the car-color-confusion video. The "quotes" pattern and embedded commands (as used in the paper-money trick) are discussed in Frogs Into Princes and Trance-Formations. (All of the above are by Bandler and Grindler, or Bandler by himself, except for NLP Volume I which is by Dilts and others.)