We know that Voldemort finds out about the Elder Wand by torturing Ollivander when even the borrowed wand (Lucius Malfoy's) fails to kill Harry. We see that Voldemort instantly becomes fascinated by the prospect of possessing the Elder Wand. Ollivander tells Voldemort that he had heard a rumor years ago that Gregorovitch used to have the Elder Wand.
He then tracks down Gregorovitch, and using torture and Legilimency, he finds out that it was stolen by "a thief". After that, through Harry's visions, we see him pondering over the identity of the thief which makes it clear that he wants it desperately.
When Harry arrives at Godric's Hollow, and Voldemort fails to kill him there again, he finally finds a picture of that thief in Bathilda's house and finds out that the thief is Gellert Grindelwald. Then Voldemort visits Nurmengard to talk to Grindelwald, and at the same time Harry, Ron and Hermione are caught by snatchers and taken to Malfoy Manor. The entire, slightly cryptic conversation between Grindelwald and Voldemort is shown in bits and pieces between the whole Malfoy Manor scene.
Closing his puffy eyes, he allowed the pain in his scar to overcome him for a moment, wanting to know what Voldemort was doing, whether he knew yet that Harry was caught. . . .
The emaciated figure stirred beneath its thin blanket and rolled over toward him, eyes opening in a skull of a face. . . . The frail man sat up, great sunken eyes fixed upon him, upon Voldemort, and then he smiled. Most of his teeth were gone. . . .
“So, you have come. I thought you would . . . one day. But your journey was pointless. I never had it.”
“You lie!”
As Harry spoke, his scar burned worse than ever, and for a few seconds he looked down, not upon the wandmaker, but on another man who was just as old, just as thin, but laughing scornfully.
“Kill me, then. Voldemort, I welcome death! But my death will not bring you what you seek. . . . There is so much you do not understand. . . . ”
He felt Voldemort’s fury, but as Hermione screamed again he shut it out, returning to the cellar and the horror of his own present.
At once, Harry’s scar felt as though it had split open again. His true surroundings vanished: He was Voldemort, and the skeletal wizard before him was laughing toothlessly at him; he was enraged at the summons he felt—he had warned them, he had told them to summon him for nothing less than Potter. If they were mistaken . . .
“Kill me, then!” demanded the old man. “You will not win, you cannot win! That wand will never, ever be yours—“ And Voldemort’s fury broke: A burst of green light filled the prison room and the frail old body was lifted from its hard bed and then fell back, lifeless, and Voldemort returned to the window, his wrath barely controllable.
Deathly Hallows. Chapter 23: Malfoy Manor
Grindelwald never tells him anything about the wand and goes as far as to lie and say that he never had it. Also, from the start of the book it had been made clear that Dumbledore and Grindelwald's duel had been very famous.
He had never thought to ask Dumbledore about his past. No doubt it would have felt strange, impertinent even, but after all, it had been common knowledge that Dumbledore had taken part in that legendary duel with Grindelwald, and Harry had not thought to ask Dumbledore what that had been like, nor about any of his other famous achievements.
Deathly Hallows. Chapter 2: In Memoriam
My doubt is why did Voldemort even bother to visit Grindelwald? Upon realizing the identity of the thief, even with his very limited understanding of wand magic, he must have put two and two together to figure out that Dumbledore was the owner of the Elder Wand. Knowing how badly he wanted to possess it, why not go directly to Hogwarts?
P.S: I know that Voldemort couldn't have predicted his conversation with Grindelwald (the fact that Grindelwald will lie and not tell him anything useful) but it still doesn't justify Voldemort's visit when he already knew that the wand was in Dumbledore's possession.
