Fxqoazh

Gollum knows what's common knowledge among the servants of Sauron

In the book The Two Towers, Sam asks Gollum more or less the same question as you're asking, in a typically suspicious manner:

‘No, no indeed,’ said Gollum. ‘Hobbits must see, must try to understand. He does not expect attack that way. His Eye is all round, but it attends more to some places than to others. He can’t see everything all at once, not yet. You see, He has conquered all the country west of the Shadowy Mountains down to the River, and He holds the bridges now. He thinks no one can come to the Moontower without fighting big battle at the bridges, or getting lots of boats which they cannot hide and He will know about.’

‘You seem to know a lot about what He’s doing and thinking,’ said Sam. ‘Have you been talking to Him lately? Or just hobnobbing with Orcs?’

‘Not nice hobbit, not sensible,’ said Gollum, giving Sam an angry glance and turning to Frodo. ‘Sméagol has talked to Orcs, yes of course, before he met master, and to many peoples: he has walked very far. And what he says now many peoples are saying. It’s here in the North that the big danger is for Him, and for us. He will come out of the Black Gate one day, one day soon. That is the only way big armies can come. But away down west He is not afraid, and there are the Silent Watchers.’

Gollum's answer makes sense, since he had spent time in Mordor previously, and must have heard a lot of chatter from various orcs during his time there.

... and the rest is easy to deduce from seeing the Haradrim.

When the Haradrim show up, close at hand to where the trio are resting, Gollum sneaks up to watch them, and the rest is simple deduction:

‘More Men going to Mordor,’ he said in a low voice. ‘Dark faces. We have not seen Men like these before, no, Sméagol has not. They are fierce. They have black eyes, and long black hair, and gold rings in their ears; yes, lots of beautiful gold. And some have red paint on their cheeks, and red cloaks; and their flags are red, and the tips of their spears; and they have round shields, yellow and black with big spikes. Not nice; very cruel wicked Men they look. Almost as bad as Orcs, and much bigger. Sméagol thinks they have come out of the South beyond the Great River’s end: they came up that road. They have passed on to the Black Gate; but more may follow. Always more people coming to Mordor. One day all the peoples will be inside.’

They are clearly allies of Sauron, from the fact that they march so openly and casually on the very border of Mordor. And they seem to be from the South, both from their appearance and the fact that they're coming up the southern road to the Morannon.

He's been hiding under a mountain for years, and when he wasn't hiding under a mountain, he was stalking the Fellowship. The point is that his activities would not put him in contact with people who would know Sauron's plans.

Bilbo was only 50 when he left on his quest. He turns 51 while riding in the barrel, so he's 51 when he arrives in Esgaroth, on Long Lake.

Bilbo then keeps the ring until his 111^th birthday, when he (quite reluctantly) leaves it to Frodo. Frodo and Bilbo shared the same birthday, so Frodo turned 33 when he received the ring.

Then Frodo has the ring for some time. He's 50 when Gandalf returns and puts it in the fire to confirm its true identity.

So, there's approximately 77 years from when Bilbo first got the ring, until Gandalf reveals to Frodo what the ring really is.

So what did Gollum do during that time? He remained in the mountains for a little of it, but only a little. Toward the beginning of The Fellowship, Gandalf says:

Oh yes, he came out. His longing for the Ring proved stronger than his fear of the orcs, or even of the light. After a year or two, he left the mountains.

So, Gollum had around 75 years to travel around middle earth, gather news and try to find Bilbo:

'[...] He found his way into Mirkwood, as one would expect.'
'Is that where you found him?' asked Frodo.
'I saw him there', answered Gandalf, 'but before that he had wandered far, following Bilbo's trail.'
'[...] from hints dropped among the snarls I even gathered this his padding feet had taken him at least to Esgaroth, and even to the streets of Dale, listening secretly and peering.'
'[...] But at last, when I had given up the chase and turned to other parts, Gollum was found. My friend [Aragorn] returned out of great perils bringing the miserable creature with him.'
"What he had been doing he would not say. He only wept and called us cruel, with many a gollum in his throat; and when we pressed him, he whined and cringed, and rubbed his long hands, as if he remembered some old torture. But I am afraid there is no possible doubt he had made his slow, sneaking way, step by step, mile by mile, south, down at last to the land of Mordor."

Summary

Gollum/Smeagol has had around 75 years to gather news of the ring, Mordor, and Sauron (and chase after Bilbo)--and he's made use of that time, traveling all over middle earth and gathering news. Further, his long association with the ring draws him to the parts of middle earth such as Mirkwood and Mordor that are closely associated with Sauron, leading to a considerable amount of information about Sauron and his intentions.

Two points:

First, how could anyone in southern Middle-Earth be unaware of this? Sauron had been stepping up his pressure on Gondor for years, and armies being gathered in to Mordor could only mean one thing. And Gollum had an established pattern of spying and listening.

Second, Gollum had previously been Sauron's captive and was tortured. Sauron had an established pattern of gloating over his captured enemies, and even if Sauron didn't monologue at Gollum, the orcs who would have been his primary jailers/torturers would have gloated. And they knew much of what was going on and gossiped. For example:

'Oho! So they haven't told you what to expect? They don't tell us all they know, do they? Not by half. But they can make mistakes, even the Top Ones can.'

'Sh, Gorbag!' Shagrat's voice was lowered, so that even with his strangely sharpened hearing Sam could only just catch what was said. 'They may, but they've got eyes and ears everywhere; some among my lot, as like as not. But there's no doubt about it, they're troubled about something. The Nazgûl down below are, by your account; and Lugbúrz is too. Something nearly slipped.'

'Nearly, you say! ' said Gorbag.

'All right,' said Shagrat, 'but we'll talk of that later: Wait till we get to the Under-way. There's a place there where we can talk a bit, while the lads go on.'