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

WARNING: Spoiler Alerts throughout this question...

Now, 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

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 is 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