What is the true definition of a witch?
A witch is simply a wise woman or man who understands mother earth, harnesses or utilizes the elements and energies within it, and unites it as a whole.
How can you become a witch?
Of course you can't just automatically be a wise person. You must study the craft, not only study but experience and live the craft.
What do witches believe in?
Witches believe what they want to believe. The general practice of a witch is harnessing and utilizing the energies within the universe manifest a result. Their belief system, however, is something only they can choose. Witches are witches. And again a witch is a wise person who understands mother earth deeply. That being said they choose their belief system such as a Wiccan Witch or a Pagan witch.
Actually, if you want to get into "true definitions" you'll need to pay attention to etymology, anthology, and how the word was originally used.
Witchcraft versus sorcery in anthology in particular. Witchcraft is a natural, inborn ability to use an invisible, internal force to cause change in the world without the need of spells, rituals, etc. Sorcery involves a learned ability to use an invisible force to cause change in the world through the use of spells, rituals, etc.
Therefore, most folks aren't witches, they are sorcerers. Especially if they require study, rituals, spells, etc, in order to practice.