It surprises me to be asked this so frequently since I thought I’d covered it in the introductory notes to each volume. Classical peoples were heavily involved in magic (as opposed to religion). This seems to have been mostly Egyptian in origin, though there are mixtures of classical religion as well as Judaism and Christianity.
Spells could be for any purpose: revenge on a thief or strayed lover, gambling success, and good health are among the range of typical examples. The person making the spell spoke it or wrote and buried it. A lot of those buried (often in a graveyard) have been discovered in modern times.
The person making the spell would get the attention of the spirits (demiurges, not the Great Gods) by addressing them in their own language. He would then tell them what he wanted them to do in common (human) language.
For the Isles series, I’ve used the ‘spirit language’ (voces mysticae in modern parlance) from real spells for the spells the wizards speak.