(From my What is Sacrifice?, with slight modifications.)
In Pollux, the phrases “to pray to the gods” and “to stretch one’s hands upward” are used as equivalents, “because we humans all stretch our hands towards heaven when we make prayers” (Pseudo-Aristotle, On the Cosmos 400a). This apparently included Jews and Christians, although neither religion now seems to employ it.
But not every prayer was necessarily attended by this large gesture. As Simon Pulleyn writes, it is more common in artistic depictions for the worshipper to raise only one hand, not above the head, but “held out in front of one in a gesture like that used by policemen to halt traffic” (Prayer in Greek Religion, 1997, p. 189). Since Plato assigns the right to the Olympian gods and the left to those of the underworld (Laws 717a), it may be that only the respective hand would be raised; or it may not. The meaning of this passage is not as clear as Pulleyn suggests.
When praying to the gods below, one might still raise the hands upwards to a cult statue (Pulleyn, p. 190), or, more intuitively, stretch them downwards, as an anonymous commentator on Vergil notes: “we invoke the gods below with hands cast down towards the earth; hence Homer has Althaea, the mother of Meleager, (pray) with hands far outstretched […] but we pray to the celestial gods with hands raised toward heaven” (Servius auctus on Aeneid 4.205). In the Homeric passage referenced (Iliad 9.658), Althaea in fact strikes the earth; the commentator’s interpretation suggests that this was (or at least, was understood as) a poetic exaggeration of the ordinary custom.
My own opinion is that, in all, one should not overthink hand gestures. The gesture of folding the hands now commonly used by Christians (at any rate by Catholics and Protestants; I do not know about other Christian groups) was apparently unknown in the Ancient Mediterranean, and so not consciously rejected by pagans; as Christians only adopted it over time, there is no obvious reason that pagans could not do so as well.
SARTRIX 