[Guinevere]

According to the Elf-centred mythology there was at first an actual Earthly Paradise, home and realm of the Valar, as a physical part of the earth.
(The Valar or "gods" are best described as angelic powers whose function was to exercise delegated authority in their spheres.)
The Valar persuaded a large part of the Elves to come and live with them in Valinor.(They were transported there on an island, Tol Eressea) Some of those Elves, however, went later back to Middle-earth.
Until the downfall of Numenor in the end of th 2nd age the world was envisaged as flat !
When the Numenoreans in their pride and folly broke the ban to sail West and tried to assault Valinor with a huge Armada (they thought they could thus gain immortality) the Valar appealed to Eru (God) and the old world was broken and changed. The earth became round, and the Immortal Lands (Valinor and Tol Eressea) were removed from the earth. But the immortal Elves who still lingered in Middle-earth in the 3rd age, could still take ship and find the "straight way" and come to the ancient West.
For the few mortals who by special grace went to Aman with the Elves, (Frodo, Bilbo, and later Gimli and eventually Sam) it didn't mean that they would become immortal though! They could only dwell there a limited time to receive peace and healing and would eventually die.

I hope this brief summary helps you to make things clearer, Etharius.
If you want to know more, you ought to read the Silmarillion, as the Lord of Angmar said.