it's actually quite simple. if you dont fret over spell speeds...(dont think about them).
the biggest card wins(usually.) its math on steroids. a 1500 attack monster is beaten by a 1900 monsters
they have attack points, and defense points. they can be played in to mmodes(the monsters) in attack or defense.
in defense you cant take damage, but you cant attack. you have magic monsters and traps. if you watch 5 episodes of the anime, you should understand it okay. (but the anime rules arent all that static. sometimes they disregard the TCG, and morph effects to fit the situation.