Zatanna Zatara makes her living as a stage magician and uses her real magical powers to fight demons and supervillains, both on her own and in the Justice League of America. Her nearly limitless powers make her one of the most powerful people in the DC Universe.
Zatanna (nicknamed "Zee") is the daughter of magician Giovanni (John) Zatara and Sindella, a sorceress of the Homo magi race. She learned magic from lost texts of Leonardo Da Vinci's--a distant relative of the Zataras--that she discovers in her father's study when he goes missing. From them she learns the family trick of casting spells by saying them backwards. After enlisting the help of various JLA members to help her find her father, she formed an association with the team, eventually joining it.
She has struggled with the moral weight her powers put on her-- and for good reason. She has occasionally used her powers to alter the memories and personalities of villains, heroes, and civilians alike, and some of her magical exploration has gotten people killed. But through it all, she remains fun-loving and optimistic.
Her new ongoing series started on Wednesday with Zatanna #1, and it's off to a great start! Zatanna's help is sought by a skeptical cop looking for answers in a bizarre mass killing of mob bosses. She quickly gets to the bottom of it, and after a tense encounter with the evil sorcerer-culprit, the chase is on-- which should give her and the cop some time to get to know each other... (To find a comic shop near you, go to ComicShopLocator.com.)
Some other Zatanna stories you might want to check out are:
Zatanna: Everyday Magic - A short graphic novel where Zee's old flame John Constantine interrupts her hectic life of touring and budding romance after his recent fling leaves him with a demon on his tail. A good, fun introduction to the character.
Seven Soldiers: Zatanna - Zatanna goes into superhero rehab after a magical experiment goes awry, killing four other magicians and stripping her of her powers. A young girl with magical powers of her own convinces Zee to take her on as an apprentice to help her fix her mistakes. Technically part of a vast crossover with six other minor superheroes, her story stands fine on its own. Unfortunately, the only way to read this story on its own is in the original four issues, readily available on eBay.
If you want to try some old-school comics and read Zatanna's first appearances, then check out JLA: Zatanna's Search. Her first storyline that ran from 1962-64, this book tells the story of how Zatanna enlisted the help of various superheroes to help her find her missing father, plus a bonus story about how she first discovered her own powers.
Zatanna: Come Together is a 1993 mini-series, her first solo venture. It's a highly experimental story about her exploring her mystical heritage from her mother's side with gorgeous art by Esteban Maroto. Again, it hasn't been released in collected form, so your best bet is to get it on eBay.