"How does the elder wand become Harry's?"

Okay, so this one is a bit tricky, I grant you, but has an answer that can be found in the text. First, let us trace its most recent lineage. Gellert Grindelwald stole the wand from Gregorovitch, a foreign wand maker. Dumbledore won the wand in his historic duel with Grindelwald. Then, we are LED to believe the wand becomes Snape's after he kills Dumbledore (Spoiler for those who have not read The Deathly Hallows, DUMBLEDORE'S DEATH WAS PLANNED!), BUT....... The wand becomes Malfoy's when he disarms Dumbledore up on the astronomy tower. It then becomes Harr'y when he overpowers Malfoy in The Room of Requirement.