Act 1.1
The play begins with a conversation between Archidamus and Camillo that reveals the situation. Polixenes, king of Bohemia is visiting his boyhood friend Leontes, king of Sicily.
"Since their more mature dignities and royal necessities made separation of their society, their encounters, though not personal, have been royally attorneyed with gifts, letters, loving embassies, that they have seemed to be together, though absent;" (1.1.24 - 29)
Polixenes' visit is the first personal encounter the two kings will have had since boyhood, making this first scene is a continuation of their "loving embassies" - their "real" meeting is yet to be witnessed. We expect something less stilted than this courtly exchange, where exaggeration ends up becoming sinister: Archidamus' gratitude is expressed with talk of spiked drinks (1.1.10-15), while, ironically, admiration of Leontes' son and heir Mamillius ends up imagining his absence - if the king had no son... (1.1.44), prefiguring his later death.
Act 1.2
When we see the reunited kings, however, they are about to separate. Polixenes has been there nine months already and wishes to leave, while Leontes wants him to stay at least a week longer. Although they are not exactly arguing - Leontes' "We'll part the time between's then: and in that / I'll no gainsaying" (1.1.17- 8) is more like bargaining - there is an awkwardness in the air, so that it is not surprising that having convinced Polixenes to stay Hermione tries to get the conversation onto a safe subject, the two kings' boyhood, hoping perhaps to include Leontes, who is rather left out. Polixenes' praise of the innocence of boyhood inevitably implies a contrast with the experience of adulthood, and Hermione picks up on this laughingly:
"Of this make no conclusion, lest you say
Your queen and I are devils" (1.1.81-2)
The laughter sours as the scene unfolds towards Leontes' jealousy: it becomes increasingly difficult for him, or anyone else, to speak innocently. Leontes says to Mamillius,
"Come captain,
we must be neat; not neat, but cleanly captain" (1.2.123-4)
His self-correction reveals that he has fallen into a state of mind where even a bad pun (neat = clean; neat = horned cattle) appears not as an accident of language but as further proof of his cuckoldry (cuckolds traditionally had horns). Autolycus calls himself a "snapper-up of unconsidered trifles", and that is exactly what Leontes is, taking seriously that which is insignificant, trifling or ornamental. No wonder that, seeing himself in Mamillius, he remarks on the,
"dagger muzzl'd
Lest it should bite its master, and so prove,
As ornaments oft do, too dangerous" (1.2.156- 8)
Leontes walks with Mamillius, leaving Hermione and Polixenes together, and watching them closely for confirmation of his suspicions, bitterly reflecting that "There have been / (Or I am much deceiv'd) cuckolds ere now" (1.2.190-1, the fact that his fate is a common one affording him poor comfort, turning the world into a "bawdy planet" (1.2.201)
"Mamillius: I am like you, they say.
Leontes: Why, that's some comfort." (1.2.2060)
Mamillius unwittingly touches exposed nerves, since his similarity to his father only emphasises Leontes' belief that his unborn child is in fact not his. Similarity more generally is a vexing subject for him because his sense of self has been wounded by his "poor part", his similarity to countless unnamed common cuckolds. He has become a stock figure, the butt of jokes and tales, hearsay and rumour, or at least that is what it seems to him "they say". When Camillo, who has been present throughout the scene, remarks innocently (but disastrously) on how difficult it was to get Polixenes to stay, Leontes is beside himself.
"They're here with me already; whisp'ring, rounding
"Sicilia is so-forth": tis far gone,
When I shall gust it last." (1.2.217-219)
Camillo is horrified at Leontes when he realises his state of mind and frankly calls it this diseased opinion. Leontes' response is a petulant denial:
"It is: you lie, you lie:
I say thou liest, Camillo, and I hate thee,
Pronounce thee a gross lout, a mindless slave,
Or else a hovering temporiser that
Canst with both eyes at once see good and evil,
Inclining to them both" (1.2. 299ff)
Camillo's desperation when he is ordered to poison Polixenes is shown when appeals to "thee" instead of the respectful "you" (324) but Leontes is convinced that his jealous madness is a state of heightened, superior perception, and even argues that since it is the last thing he would want to believe, the fact that he believes it shows it is true. Camillo is left with the impossible choice of disobeying his master or committing regicide when Polixenes enters and asks him what is going on, having sensed a change in Leontes' manner. Camillo, unable to lie to him, reveals the poison plot and the reason for it, and Polixenes decides to flee with Camillo.