In Book 10 of The Odyssey, how does Odysseus get Circe to release his men?
When Odysseus landed on Circe's island, he spotted the smoke coming from Circe's fireplace and sent his second-in-command, Eurylochus, to investigate with half his sailors. Circe, a nymph and sorceress, used a combination of drugged wine and a magic wand to turn them into swine. Eurylochus managed to escape, not having drunk the wine, and warned Odysseus.
As Odysseus was on the way to rescue the men, the god Hermes warned him of his peril and gave him the herb "moly," which can only be harvested by a god, not a human:
Its root is black and its flower white as milk and the gods call it moly. Dangerous for a mortal man to pluck from the soil but not for deathless gods...
Odysseus takes the herb, and when neither the drugged wine nor wand affect him, to Circe's surprise, he pulls out his sword and threatens her, demanding she release his men. Circe apparently finds this behavior alluring and seduces Odysseus, after she has sworn binding oaths not to harm him or his men. After a brief romantic interlude, Circe frees the men and invites them all to a feast.
Odysseus got Circe to release his men from the magic spell by force and charm and with the help of the god Hermes.
Circe had turned Odysseus's men into pigs by the use of drugged wine and magic. Hermes gave Odysseus a plant that would keep him safe from the drugged wine. Odysseus then went to Circe and drank of the drugged wine. It did not affect him and he forced her to swear not to try to harm him again. The two of them ended up sleeping together and Circe falls for Odysseus. When Odysseus continues not to trust her, she turns his men back into men because she wants him to approve of her.
So, Odysseus uses a combination of his charm and force, along with help from Hermes, to get Circe to free his men.