It's not by brute-force attacks. Oh, he has no problem with those - the attacks on Eregion, the Last Alliance, Gondor - but they're very much his backup plan. At no point has Sauron engaged in warfare as his preferred option.
What he does instead is attempt to seduce his enemies, and he does this in a very specific way: by giving them what they want, and then twisting it until they give him what he wants. Let's look at a few examples:
We actually see this technique four times in the Lay of Leithian:
The very first thing Sauron does on capturing Finrod and Beren is offer to let them go - precisely what they want! But in order to do so, they have to swear their alliegance to Morgoth: Death to light, to law, to love! Cursed be moon and stars above! He will grant freedom, but only if they blaspheme before the One.
When that fails, Sauron engages in exactly the kind of duel Finrod would have the best chance at: one of music and song. The Elvenking invokes the light of Aman, a more powerful magic than Sauron could possibly bring to bear - but the Lord of Wolves has a secret weapon. He turns the light of the Trees into the fires of the Kinslaying, and Finrod fails.
Thirdly, Sauron takes the secrecy the party had put their trust in, and twists it, too. They are hidden away, shut into darkness, nameless, to be devoured anonymously by werewolves. They have exactly what they sought, and it is cruel.
Finally, Sauron's tower is attacked by Huan and Luthien. The Lord of Dogs wants to fight werewolves; Luthien wants Sauron to come out and surrender himself. He does both, exactly as they desire - but he tries to turn himself into the wolf that can defeat Huan, twisting their plan into the means of their defeat. He fails, but it's very much his goal.
Moving on to the Second Age, Sauron comes to the doors of the jewel-smiths of Eregion as a smith himself. They want knowledge and craft, and he provides it - but in the end, he uses their own skills against them, forging the One Ring to control the rings the elves made. Only once his plan fails, and Celebrimbor sends the Elven rings away, does he resort to outright war.
What does Ar-Pharazon the Golden want? Victory, conquest, submission - and Sauron gives him all three. But once he is taken to Numenor, he warps the king's desires. Worship of Melkor can give you victory. The Undying Lands are ripe for conquest. The Valar themselves should submit to you. So Numenor sails West, and Sauron has his revenge.
Saruman desires power and strength. Sauron is willing to provide them - armies of orcs that will do the White Wizard's bidding. His price is simply that Saruman use that power in his service, not that of the West. A simple bargain, no...?
Finally, we come to Denethor. Denethor's pride demands one thing: that he be the sole guardian of the West against the assaults of Sauron. And, true to form, Sauron gives him exactly that: a view of events through his Palantir that shows no hope other than Gondor. But then he tweaks things further, showing the Steward that even the strength of Gondor is failing. The man who secretly wants to be the last hope is left with no hope; he cannot concieve that any other power will break the siege of Minas Tirith, because Sauron has convinced him - as he wished to be convinced - that there is no-one else who can.