How did the elves know where Sauron crafted the One Ring?

Question

After Sauron finished crafting the One Ring and placed it upon his finger the elves knew of his treachery, and his intentions. But how did the elves know where Sauron crafted the One Ring? And how did they know that throwing the One Ring into the fires of Mount Doom would destroy the One Ring? How did they know that there was no other way in existence to destroy the ring?

No one ever tried to destroy the One Ring before. Isildur took it shortly after cutting it free from Sauron's hand. The ring corrupted him and Isildur would never allow it to be handled by anyone else. From there he lost the ring when it betrayed him in the river. After that it came into the possession of Gollum / Sméagol. We know Gollum never tried to destroy it. Then Bilbo found it. Other than when Gandalf threw the ring into the fireplace no one ever tried to harm the ring.

And this leads me back to the beginning. How did the Elves know where the One Ring was forged, and how did they know that the fires of Mount Doom were the only way to destroy the One Ring?

Answer 1

Possible Answer;

When Sauron put on the One Ring, the Elves were "aware" of him. There was a connection between the Rings, and the elves might have been aware of him through this.

Answer 2

In "The Return of the Shadow," it's stated that Sauron:

made many rings, and he dealt them out lavishly, so that they might be spread abroad to ensnare folk.

Although he forged the One Ring in secret, according to "Of the Rings of Power and the Third Age", he was in Mordor, wherein lies Orodruin, when he did his forgings.

Indeed for that reason Sauron had set there his dwelling long before, for he used the fire that welled there from the heart of the earth in his sorceries and in his forging; and in the midst of the Land of Mordor he had fashioned the Ruling Ring.

So, as others have alluded to and as discussed in the "Of the Rings of Power and the Third Age,"

As soon as Sauron set the One Ring upon his finger they [the elves] were aware of him; and they knew him, and perceived that he would be master of them, and of all that they wrought.

By the time of the third-age and the Fellowship, it had been handed down in verse:

Three Rings for the Elven-kings under the sky,
Seven for the Dwarf-lords in their halls of stone,
Nine for Mortal Men doomed to die,
One for the Dark Lord on his dark throne
In the Land of Mordor where the Shadows lie.
One Ring to rule them all, One Ring to find them,
One Ring to bring them all and in the darkness bind them
In the Land of Mordor where the Shadows lie.

As for how they knew that that throwing it into the fires of Mount Doom would destroy the ring? This is speculative, but the elves were supreme craftsman and it may be that knowing about forging, they figured the fires of Mount Doom were hot enough to forge the ring and to undo it, as well. This may not have been the only way, but perhaps they thought it the surest way.

Answer 3

Another Possible Answer:

In LoTR the general understanding is that forging the Great Ring involved a heat level greater than or equal to that of Ancalagon the Black. The only thing hotter than Ancalagon is Mount Doom; since Ancalagon wasn't available, the Ring had to have been forged there.