Why did Dumbledore 'put on' the Resurrection Stone (Ring)?

Question

Dumbledore put on Marvolo's ring, knowing that it was the Resurrection Stone which was on the ring. He also knew (even though he "lost his head" in his excitement to see his family again) that the ring was a Horcrux and would "surely carry a curse":

When I discovered it, after all those years, buried in the abandoned home of the Gaunts - the Hallow I had craved most of all, though in my youth I had wanted it for very different reasons - I lost my head, Harry. I quite forgot that it was now a Horcrux, that the ring was sure to carry a curse. I picked it up, and I put it on...

-Deathly Hallows, Ch 35 - KING'S CROSS

Now when Harry realised that the Resurrection Stone was inside the Snitch, all he had to do was turn it three times for it to 'work':

He closed his eyes and turned the stone over in his hand three times. He knew it had happened, because he heard slight movements around him that suggested frail bodies shifting their footing on the earthy, twig-strewn ground that marked the outer edge of the forest.

-Deathly Hallows, Ch 34 - THE FOREST AGAIN

I may be missing something, but did Dumbledore incorrectly use the Resurrection Stone?

or did Harry just 'think' that he had to turn it thrice?

I'm assuming the answer may have been that Dumbledore wanted to have the ring on, and then turn it thrice whenever he felt like conjuring up his family; or that he simply "lost his head"; but he surely didn't need to put it on right?

What is the correct way to use the Resurrection Stone?

Answer 1

Dumbledore did indeed use the stone incorrectly. In his excitement to recall his lost family, he let himself forget that the ring was a Horcrux and he simply put the ring on. However since this was, at the time, one of Voldemort's horcruxes, putting the ring on triggered the curse that would have killed Dumbledore, which is why he made Snape promise to kill him rather than to allow Draco to do it.

After Dumbledore recovered the ring, he destroyed the Horcrux with the Sword of Gryffindor, which is to say he specifically destroyed the ring. The resurrection stone was not destroyed. The stone was then placed into the Golden Snitch for Harry to find.

Now, back to your question about whether he used it correctly. According to the "Tale of the Three Brothers", when Cadmus Peverell was first granted the stone by Death, he turned it thrice in hand and recalled his long-lost love from the grave. This established that turning the ring thrice in hand is the method of using the stone, and since the "Tale of the Three Brothers" is the source of Harry's only knowledge about the stone, he turned it thrice in hand to recall his loved ones prior to sacrificing himself to Voldemort.

Also, Tom Riddle was known to wear the Gaunt Ring openly during his time at Hogwarts, so it is unlikely that simply wearing the ring would allow one to use the Resurrection Stone

Answer 2

As cbornsh2 perfectly explained in their answer, Dumbledore did use the stone incorrectly. That answers the question you highlighted at the end ("What is the correct way to use the Resurrection Stone?"). But if your main question is the title: "Why did he put the ring on?" then maybe there is another answer.

We assume that Dumbledore wanted to use the stone, but what if that is not the case?

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In your quote, Dumbledore states that "through [his] youth [he] had wanted it for very different reasons":

"When I discovered it, after all those years, buried in the abandoned home of the Gaunts - the Hallow I had craved most of all, though in my youth I had wanted it for very different reasons - I lost my head, Harry. I quite forgot that it was now a Horcrux, that the ring was sure to carry a curse. I picked it up, and I put it on..."

-- Harry Potter and the Deathly Hallows - Chapter 35: King's Cross

His first reason was his and Grindelwald's obsession with the Deathly Hallows, which is of course related to his second, later reason: seeing his mother and sister again after their deaths. Maybe the reason driving him at that moment is not the one we believe.

The Resurrection Stone was the last Hallow that Dumbledore had yet to find. We can even argue it was the only one he didn't control : the Wand was his and even though Harry owned the Cloak, Dumbledore had had it up until Harry's first year, and he could easily have gotten a hold of it again (asking Harry to lend it to him or to the Order for example).

"I was fit only to possess the meanest of them, the least extraordinary. I was fit to own the Elder Wand, and not boast of it, and not to kill with it. I was permitted to tame and use it, because I took it, not for gain, but to save others from it."

"You have guessed, I know, why the Cloak was in my possession on the night your parents died. James had showed it to me just a few days previously."

-- both quotes from Harry Potter and the Deathly Hallows - Chapter 35: King's Cross

Then, maybe the reason he put the ring on was something else.

When he says that he lost his head, he doesn't mean "I lost my head, I'm old, I didn't remember how it works."

Remember that he and Grindelwald spent months researching everything there was to be known about these Hallows. Of course Dumbledore, one of the most powerful wizards alive, didn't just forget such a basic piece of information about his old obsession just because of emotion (even Harry remembered it !). Dumbledore is often described as old but never as senile, forgetful or easily distracted by emotions (that would be quite impractical in duels).

I believe he means "I lost my head, my old demons came back and for a moment I was attracted to the power of the Hallows again."

We have seen with the Cloak that even after he renounced his earlier beliefs and stopped his quest for the Hallows, they still had power over him.

"I could not resist, could not help taking a closer look ... [...] and then your father died, and I had two Hallows at last, all to myself!'

-- Harry Potter and the Deathly Hallows - Chapter 35: King's Cross

Even though we could logically think that he wanted to use the Stone to see his family, I believe that he lost control again, like when faced with the Cloak. And that is why he put the ring on instead of turning it in his hand which he knew was the correct way to use it.

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He put the ring on because what he wanted was not to use the Stone, but to own and control it, as one of the object that could make him the Master of Death.

“I was such a fool, Harry. After all those years I had learned nothing. I was unworthy to unite the Deathly Hallows, I had proved it time and again, and here was final proof.”

-- Harry Potter and the Deathly Hallows - Chapter 35: King's Cross

Answer 3

I was just relistening the last book and a thought crossed my mind.

Every Horcrux put up a fight when it sensed that it was close to being destroyed.

So maybe the piece of soul in the ring tempted Dumbledore to put it on, by showing him the people he had lost.

Why did he not tell Snape or Harry? He was probably embarrassed to have been tempted by Voldemort.