Here is a blurb taken from Wizards of the coast on how the game works: 

"The beginning rules are fairly simple. You and your opponent are wizards dueling at Hogwart's School of Witchcraft and Wizardry. During the duel, you can use magical creatures or spells to "damage" your opponent. For each point of damage you do, your opponent has to discard that many cards from his or her deck. You win the game when your opponent's deck runs out of cards!"

No-brainer huh? In fact I was able to teach several people who weren't Harry Potter fans how to play it with me in a matter of 2 games.  Now they run whenever they see me carrying it around because I'll make them play it over and over, but they still had fun the first couple times hehehe.  Of course the game does have a few other rules to it during play, which make it hard enough that anyone under 9 definitely wouldn't be able to figure it out, but it does make a good family game.

If you'd like to try Harry Potter, start off with the basic 2 player starter pack.  It's about $10, has 40 cards, rules and a play mat.  If you like it, move on to the regular boosters.  If you really like those, then you can move onto the expansion boosters like Diagon Alley, Quidditch Cup and Adventures at Hogwarts.  These boosters add more spells and creatures and characters to the game, making it 10 times more fun. Heck I just have fun creating custom decks and testing them against each other.  

The art is really cute, and based more on the book than the movie.