A witch is a practitioner of magic that is able to manipulate reality through magic, capable of doing almost anything. A male witch is called a warlock. They can cast spells, and make potions. Witches and warlocks are long-lived, as aging takes centuries, while from their perspective, mortals age overnight. Samantha is at least 500 years old, but looks like she's in her twenties. Witches are naturally born with their powers and can pass them down to their offspring. Witches and warlocks also look and dress like normal people blowing the theory of stereotypical witches created by mortals.
The first stage of witchcraft is wishcraft which is wishing someone you love to be with you. Tabitha first displayed this in "It's Wishcraft" when she wanted her daddy to be with her and "popped him" to her room. Adam used this power in "Adam Warlock or Washout" and teleported his mommy to the kitchen with him.
Witchcraft is also a skill because the more a witch practices the more powerful they become. Witches learn how to use their powers at a young age like Tabitha and Adam as they often do strange things uncontrollably. Witches usually inherit their powers from their witch/warlock parents. The gift of magic is great indeed but it can cause problems and become dangerous.
A witch or warlock can cast their spells in several different ways to show signs of her/him using witchcraft. One famous way is by twitching your nose like Samantha often does when using her powers. Another way is by using hand gestures such as pointing or snapping your fingers. Witches can also speak incantations that rhyme and cause an supernatural affect. When a witch or warlock casted magic spells the show featured music to highlight the magic.
Witches and warlocks can use their magical powers anytime they want, but they tend to not use their magic in front of mortals except Darrin. The Witches' Council can take away a witch's witchcraft if a warlock or witch fails to obey the council's rules or by giving up magic on their own.