"All right, you want to fry a witch? I'll give you
a witch. Goddess Hecate, work thy will."
Amy is the daughter of Sunnydale High's Cheerleading Champion Catherine Madison. Her mother figured heavily in her life after her father left them when she was younger. But Catherine figured in more ways than one. A woman who wished to relive her glory days, Catherine pushed her daughter into Cheerleading, a role that Amy didn't want to play.
Annoyed with her daughter's lack of love for cheerleading, Catherine turned to the dark said and dabbled in Black Magic, the culmination of her studies was the ability to swap bodies with her daughter and become the head cheerleader again, literally reliving her glory days.
But that in itself was laced with problems as Catherine had trouble controlling her new body and then there was the homework too, which she took home and got Amy to do (so she wasn't neglecting her studies). Catherine wasn't happy with her role as third alternate and used her witchcraft skills to injure the other girls on the squad until she was on the team.
Eventually, Buffy and Giles worked out what was going on and was able to reverse the spells, putting Amy back in her own body. Catherine, not happy with this tried to cast a spell on Buffy, which she blocked and Catherine magicked herself into her own Cheerleading trophy, which has pride of place in the Sunnydale High trophy cabinet.
Amy then moved in with her dad and was very happy. She didn't forget her mother though and took up spellcasting. This brought her to Xander's attention when he saw her cast a spell on a teacher to make her believe that Amy had handed in her homework. Xander did a spot of blackmail and got Amy to cast that infamous love spell on Cordelia which backfired as well as turning Buffy into a rat.
This didn't put her off practicing magic and in her senior year she formed a coven (of sorts) with Willow (who was now following in Jenny Calendar's footstpes) and a boy called Michael. They didn't cast any interesting spells, just small forseeing and the like, but when the Gingerbread demon came to town and influenced the adults to start a witchhunt, Willow and Amy were the first taken and along with Buffy were going to be burned at the stake.
You can't fault Amy for being brave in the face of death as she threatened to turn the adult population buring her into frogs, but only succeeding in turning herself into a rat.
Unfortunately, Willow's powers are not strong enough to turn her back and apart from one occassion where Amy was turned back for a couple of seconds (in Something Blue), Amy has been spending her days running on her little wheel and really only doing ratty things.