Hypnosis is real. Hypnotism is the act of deliberately putting oneself or others into an increased state of hypnosis, and is also real.
The best description I've heard of hypnosis is that it's a bit like watching a film that has some emotional impact. Maybe it's making you cry. You're choosing to have those emotions. You can stop at any time! But you're enjoying that journey so you keep doing it.
Hypnosis is the same kind of level of engagement, but you're making the pictures. With a hypnotherapist or stage hypnotist, they're helping you set the scene; with self-hypnosis you're setting it for yourself.
Hypnosis is basically a state in which your unconscious and conscious mind are communicating more freely (there's not really any such separation, but this is how we model it). Everyone is always communicating like this to some degree, unless they're unconscious or in non-dreaming sleep, so you're always hypnotised! This is why things like placebos work. Hypnosis has been described as "the great mega-placebo".
There are five levels of hypnotic state (I can't remember the clinical descriptions exactly, so these are approximate):
Ordinary alertness. Things like positive visualization and Cognitive Behaviour Therapy still work (hypnotherapy is a lot like CBT done in trance).
Engaged, "in the flow", zoning out. A lot of people get this when they're running, etc.
First level of "trance"; ideally used for hypnotherapy. You remember what happened (replaying the memories helps reinforce the therapy).
Deeper trance. Used by stage hypnotists. You won't remember what happened.
There's a really deep level of trance in which your brain is having so much fun that it lasts until you either fall asleep, or a hypnotherapist tricks your brain into coming back up. (Don't worry; you always fall asleep eventually.)
If you want to use hypnosis to help yourself, there are a few simple things you can do:
Focus on positives. If you want to lose weight or give up smoking for example, think about what it will get for you. Do you want to fit into those jeans? Go for a run? Breathe and feel your lungs fill with clean air?
Practice the above.
Then go find a video or book that teaches you how to go into trance and practice it. The more you do it, the easier it becomes. It's hugely fun and powerful.
Source: Trained in hypnotherapy, never got the qualifications (it was helpful for my coaching-based profession).