If Aman was "taken away" at the fall of Númenor, where do the Elves (and others) sail to at the end of "Lord of the Rings?"

Question

To quote from the Akallabêth (from The Silmarillion):

"But the land of Aman and Eressea of the Eldar were taken away and removed beyond the reach of Men for ever."

And indeed, when Men tried to sail West afterwards, they noticed that Arda was round. So where exactly do the Elves and the ring-bearers sail to at the end of the Third Age? Do the Valar just pluck Western-bound ships out of the sea and bring them to wherever Aman exists? Because exist it certainly still does, to quote again from Akallabêth:

"... and the Land of Aman is taken away, and in the world of this present darkness they cannot be found. Yet once they were, and therefore they still are, in true being and in the whole shape of the world as at first it was devised."

Answer 1

The theory of Men is that there exists a special, magical route that only the Elves know how to follow:

[T]he loremasters of Men said that a Straight Road must still be, for those that were permitted to find it. And they taught that, while the new world fell away, the old road and the path of the memory of the West still went on, as it were a mighty bridge invisible that passed through the air of breath and of flight (which were bent now as the world was bent), and traversed Ilmen which flesh unaided cannot endure, until it came to Tol Eressëa, the Lonely Isle, and maybe even beyond, to Valinor

^{The Silmarillion IV Akallabêth}

However, it's never made clear exactly how this works; whether it's truly a magical heading that only the Elves know, or whether it's a property of their ships, or whether the Valar themselves literally pluck permitted ships out of the sea.

Regardless of exactly how they do it, it's beyond question that the Elves are really going back to the Undying Lands; from Tolkien's Letters, for example:

Only the 'immortals', the lingering Elves, may still if they will, wearying of the circle of the world, take ship and find the 'straight way', and come to the ancient or True West, and be at peace.

^{The Letters of J.R.R. Tolkien 131: To Milton Waldman. 1951}

Answer 2

In the history of Arda, the Teleri were the Third Kindred of the Eldar. The Teleri built the first ships in Arda- in the First Age of Stars. After the Change of the World, the swan-ships of the Teleri were the only ships that could reach Aman.