[The Saucepan Man]

How could Gollum know the whereabouts of the Shire?

Sorry, akhtene, I should have made myself clearer but I didn't have the book to hand and could not remember exactly how it was that Gollum lied to Sauron (which is why I expressed it rather vaguely).

You are right, he did not know where the Shire was. But he made out to Sauron that he did, telling him that it was near to the Gladden Fields. The relevant section from UT is as follows:

Now Sauron had never paid heed to the 'halflings', even if he had heard of them, and he did not yet know where their land lay. From Gollum, even under pain, he could not get any clear account, both because Gollum indeed had no certain knowledge himself, and because what he knew he falsified ... Then he [Gollum] became filled with a hatred of Sauron even greater than his terror, seeing in him truly his greatest enemy and rival. Thus it was that he dared to pretend that he believed that the the land of the Halflings was near to the places where he had once dwelt beside the banks of the Gladden.

In consequence, when they commence their hunt for the Ring, the Nazgul first head off up the Anduin. Thus, Gollum's deceit of Sauron actually (albeit unwittingly) saves Frodo's life and prevents the Ring from falling into Sauron's hands at the outset for, had the Nazgul arrived in the Shire much earlier, they would almost certainly have killed Frodo and seized the Ring.