After a short hiatus from the romance between our title characters, we find ourselves once again in the company of the smooth-talking Pandarus. He meets with Helen and Paris, both of whom are wholly unconcerned with the brutal realities of the Trojan War and are spending their days dallying with musicians. Pandarus comes to ask Paris to make an excuse to Priam for Troilus' absence from their company the coming night. Paris and Helen both know that the reason for this is Troilus' affair with Cressida, though Pandarus denies this when asked outright. Helen convinces Pandarus to sing them a bawdy song full of double entendres and she and Paris retire, presumably to have sex.
In the interval between Acts One and Three, Pandarus has apparently executed his office well. He has arranged a tryst for Troilus and Cressida in his garden. Both Troilus and Cressida are taciturn at first, in sharp contrast to the glib and bawdy Pandarus, though they settle into their roles as lovers in time. They discuss the nature of love - the difficulty of living up to the lofty oaths that love inspires in lovers, the ardency of their love for each other. Troilus declares that he will be true to his most outrageous and seemingly hyperbolic oaths. Cressida, for her part, spends much time and thought watching her words. The three seal their union by declaring that their names will go down in history: Troilus states that "true as Troilus" will be his heritage; Cressida declares that if she proves untrue, then women will be called "false as Cressid"; Pandarus says that if their union is not permanent, then all who bring false lovers together will be called "Pandars."
Pandarus is not the only one "trading" Cressida; on the other side of the Trojan walls, Cressida's father Calchas is bargaining for his daughter. Agamemnon declares that as payment for Calchas' defection, they will return a captured Trojan prisoner, Antenor, in return for Cressida. Meanwhile, Ulysses' plan to engender jealousy in Achilles is taking shape. He has Agamemnon, Nestor, Menelaus, and Ajax pass by Achilles' tent without paying proper respects, as though they no longer care whether or not he fights. Ulysses then approaches Achilles and remarks in a roundabout way that honor and glory can only survive if they are constantly renewed by action; reputation fades when the glorious rest on their past glories. Ulysses' ploy works, and Achilles sends Patroclus to request that Hector have dinner with him following his challenge with Ajax. Thersites, Patroclus, and Achilles then close Act Three with an impromptu play lampooning Ajax' stupidity.
The central scene of Act Three, and quite possibly the central scene of the play, is the tryst in the garden with Troilus, Cressida, and Pandarus. The complexities of this scene have inspired reams of commentary, but one of the chief things to notice about this meeting is how, despite of the intensity of their interaction, Troilus and Cressida's language is always pitched at a philosophical level. For Troilus, contact with Cressida is palpably paradoxical: he has built up Cressida in his imagination as the pinnacle of womanhood; he has worked up a desire for her that consumes his entire imagination. How can the actual moment of contact - or of lovemaking - compare with the unlimited powers of the imagination? Troilus swears that this paradox is no barrier to their love, but Cressida is more cautious. She knows, as a woman, precisely what Troilus suggests - that there is more power in imagined desire than in satisfied desire. As long as she is able to hold off Troilus' suit, she retains her power. Now, she fears that giving in to him means giving up this control. Cressida expresses this fear, in part, by constantly directing her attention to her own language. When she confesses that she always loved Troilus despite her performance to the contrary, she says, "See, we fools! / Why have I blabbed? Who shall be true to us / When we are so unsecret to ourselves?" Cressida sees honesty as the enemy of her power to hold Troilus' interest. Indeed, language itself, insofar as it exposes her vulnerabilities, weakens her in her own eyes. Troilus, on the other hand, professes that her honesty only strengthens his love for her, and that they will strive to be as "simple" and undeceiving to one another as they are able.
Fittingly, the scene ends with a definitional moment. Troilus, Cressida and Pandarus, in turn, declare that they will lend their names to history. As Pandarus puts it: "Let all constant men be Troiluses, all false women Cressids, and all brokers-between Pandars!" This would have been the height of irony to Shakespeare's audience, as to them the story of Troilus and Cressida was already well known, and indeed, false women were called Cressids, true men Troiluses, and brokers-between Pandars. (We still call such men panderers in modern English.) Thus the scene - and the play as a whole - is a kind of philosophical "Just So" story, demonstrating how language came to be as it was in Jacobean England.
And language is a slippery business, as we see not only in the Troilus-Cressida-Pandarus scene (and in the subsequent action of that plot) but also in Ulysses' talk with Achilles. Ulysses speech about the mutability of the world's opinion, and the constant need to reaffirm reputation with fresh actions, is, once again, a grand ploy. As in his speech about rank, Ulysses has the gift of appearing to discourse on general subjects when in fact he is simply serving his own ends. One of the ironies of the speech is that while Ulysses appears to rail against those who have forgotten Achilles for Ajax, he is in fact railing against a performance of his own staging. Achilles isn't really forgotten; he just needs to believe that he has been. In truth, the fact that the world appears to have forgotten Achilles is evidence that it hasn't; to the Greeks, it is worth putting on this vast charade just to have him back in battle. Ultimately Ulysses arranges a demonstration of the evils of changeable opinion (which hasn't really been changed) in order to...change Achilles' opinion.