Different types of hypnosis are stage hypnosis, covert hypnosis (for persuasion), self hypnosis, and hypnosis for specific issues such as weight loss or smoking cessation.
Hypnotherapy is medical in nature, stage hypnosis, however, is a performing art.
Stage hypnosis is typically performed on a stage, in front of a crowd or audience, for entertainment. This might happen in a dedicated venue, or in one simply rented or hired out for the performance.
The first stage iof hypnosis is Induction. It's sometimes characterised by the click of fingers. It's a stimulation of fight or flight response and moves the subject into an altered state. Some good examples are here: http://www.youtube.com/watch?v=swsLU9T1NjA&feature=channel_page Generally a deepening process (getting the subject more deeply into hypnosis) follows - and then therapy or something entertaining in the case of stage hypnosis.
Are you asking how to use hypnosis to hypnotize someone? This is a very broad question, it really depends on what you are trying to accomplish. If you are taking a more stage-like approach, you would most likely be interested in covert hypnosis, or sleight of mouth or conversational hypnosis. If you were wanting to use it to help someone with a phobia, quit smoking, lose weight, etc you would be using a different type of hypnosis, for hypnotherapy.
Maybe as a stage act, playing around but you will never get anyone to submit their full willpower to you using hypnosis.
Some experts in hypnosis can use the techniques of hypnosis to hypnotize someone instantly through conversation. This is called covert hypnosis. For more information on covert hypnosis and other forms of hypnosis visit hypnotizepro.com
There is no TM for Hypnosis in any of the versions of the game. Unfortunately, the only way to learn hypnosis is through breeding or your Pokemon leveling up. Level up haunter and it might get hypnosis.
You can get hypnosis training at local shops, or by a trained professional. Hypnosis training can be attained by going to many institutions in California, home of hypnosis training.
Hypnosis is not a TM.
Trance is a state of hypnosis.
Magicians can put people in a trance by using stage hypnosis, which is basically a trade secret that they never want to reveal to the audience of course.