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When Samwise Gamgee and Frodo Baggins spy on the Haradrim army and their oliphaunts, Gollum explains why they are marching north.

Samwise: Who are they?

Gollum: Wicked men. Servants of Sauron. They are called to Mordor. The Dark One is gathering all armies to him. If he is not now, he will soon be ready.

Samwise: Ready to do what?

Gollum: To make his war. The last war that will cover all the world in shadow.

Gollum correctly knows Sauron's plans and that the Haradrim are his servants.

How could he know all this? 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.

The quotes are from the movie, but I don't know if Gollum explains all this in the books too. If you can answer from the books, that would be better than relying on just the movies.

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.

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.'