Going over the sea?

Why and what exactly happens when they go over the from the grey havens? Is there a destination? Is it the same when Legolas and Gimli go many years later? Thanks.

Also, is there a Tolkien or LOTR faq on the book itself? Thanks.

I believe when they travel over the seas, they eventually reach the Undying Lands. If you've read the Silmarillion this is detailed there.

but why do they go? Frodo in particular, and also Gandalf, elrond, etc. Gandalf's job is done, I know, but the others?

They went to Valinor where all elves go. The only Tolkien faq I've found (even though I'm sure there are many) is here www.daimi.aau.dk/~bouvin/tolkienfaq.html

I suggest you read the silmarillion, you'll most probably find many of your answers there.

I like to think of it as going to a pre-heaven.

Well... elves do not go to heaven...
That's men gift.

They would of gone to Eressa because mortals weren't allowed in Valinor

In some rare exceptions....