Yes, Light Yagami dies in the last episode of the Death Note anime. He was shot multiple times, then he ran off and died on a staircase of some random building...
Depends wether you're asking about the Anime or the Manga. But in the anime he dies in the very last episode. (I'd imagine that he would die in the last volume of the manga)
He gets killed by Ryuk, i the begining ryuk tells light that if he writes in ryuks death note, when light dies it will be by that death note by ryuk. no quotes but that basicly what happens.