In The Lord of the Rings films, Sauron has an army he is controlling to do his bidding.
But he is only a great big eyeball.
So how can he tell them what to do?
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Sauron isn't really a giant eyeball, as compelling as that image might be. This answer raises the point that as the Necromancer of Dol Guldur, he had already taken shape decades before the War of the Ring, even though his shape wasn't as mighty as the one he assumed at the end of the Second Age. Still, even as a cloaked and hooded figure, he could give out orders.
Additionally, even if mostly noncorporeal, Sauron could and did work through lieutenants and intermediaries. The Witch-king of Angmar led the Nazgûl on Sauron's orders, whether they were communicated face-to-face or not. Similarly, heralds such as the Mouth of Sauron did his bidding. If he could manipulate and control Saruman and Denethor via the palantíri, there's no reason to assume he could not communicate with others as well.
As you can see from this scene in the extended edition, Sauron is perfectly capable of communicating in English, in this case via a palantír.
When Aragorn threatens him with the Sword of Elendil, Sauron shows him an image of Arwen's corpse and demands that he...
Think of it, and bow.
I think we can reasonably assume that he either uses telepathy (or possibly another palantír) to communicate his wishes to his various troops, his wraith-lords and his spokeperson, the 'Mouth of Sauron' or simply turned into an elemental being, as he did in the Hobbit trilogy.
Your question can be interpreted in two ways:
How can he communicate?
That seems sufficient, especially when you consider the ability of those beings to pass on orders and take initiative. The Witch-king seems quite capable of running an entire campaign with no supervision.
Now for the why:
That should be reason enough to listen to his commands, assuming you're anywhere near his influence.