There are entire books of them. Cunninham's Encyclopedia of Crystal, Gem and Metal Magic is a good start. I have personally been collecting my list for over ten years and have gathered information (some of it conflicting) from dozens of sources.
First of all, it is a matter of believe, because it can't be proven, and will not be proven, even if it exists. Because, how are you mathematically going to prove the fact that people can cure wounds...
Study all about magic. and you will get 'pretend' magic powers.
Not everyone can be a wizard if you believe it will work then you can be a wizard. There are no witches because someone says they are...
The extent of a person's magic powers depends on experience. If you are looking to cast a spell yourself, generally you will not be able to get results if you have never done it before. So much goes...