How Did Lord Voldemort Die In Harry Potter 7?

In order for Voldemort to be killed and remain dead, the "horcruxes" which he had first created had to be destroyed, so that he could not hold onto the parts of himself hidden in them and so come back to life.

At the end of the book there were two horcruxes left.  One was Harry himself and the other was Voldemort's pet snake, Nagini.  By this time, Harry realised he would have to die in order for Voldemort to be defeated, so he presented himself to Voldemort to be killed by the avada kedavra curse without a fight.  He apparently died and came back to life again, but continued to feign death.  Voldemort commanded Hagrid to carry his body back to Hogwarts.  When he arrived, in triumph as he thought, Voldemort singled out Neville Longbottom as an example.  He put a body bind curse on him and had someone ram the sorting hat down on the top of his head.  It was then set on fire.  While nobody was watching him, Harry put on his invisibility cloak.  Neville broke free of the body-bind curse, threw off the hat and pulled the sword of Gryffindor from it.  He immediately used the sword to behead Nagini.  At this point everyone realised Harry's body had disappeared and the fighting between the Death Eaters and the Hogwarts people started up again.  Finally, Harry and Voldemort met in a duel.  Voldemort used the Avada Kedavra spell and Harry used Expelliarmus.  The two spells collided in mid-air.  Voldemort's curse rebounded on him, slaying him instantly, while his wand sailed into Harry's outstretched free hand.  

Voldemort was dead, with no hope of coming back to life.  The battle was over.