The cure for lycanthropy, refereed to as "plasma therapy", was first theorized by the British Men of Letters in the 1930's. Their experiments used the blood of sire werewolves to successfully reverse the early stages of lycanthropy in one out of nine mice. The therapy would be attempted on a human once, which caused the subject to die in agony. After the failure of the human trial, the research into the cure was abandoned in favor of killing werewolves outright.
The ingredients to the cure are unknown outside of the blood of the sire werewolf. It appears live blood is required for the cure to be effective, as shown by Claire surviving being administered the cure. Much like the cure for vampirism, the infected go through an agonizing ordeal as the cure reverses the transformation, ending when their claws and teeth retract and their eyes return to normal. The cure also depends on the infected refusing to feed, as feasting on a human heart will make the transformation permanent.
Some hunters, including John Winchester, theorized that killing the werewolf that bit them -- "severing the bloodline" -- would cause the person to revert back to a human, however the theory was disproven. For centuries, hunters originally believed that lycanthropy had no cure, until Sam reads up on lore books from the London Chapterhouse.
While reading through Mick Davies' lore books, Sam discovered that the British Men of Letters were working on a treatment for werewolves known as "plasma therapy" in the '30s. Mick, however, tells Sam that the experiments were useless.
After Claire gets bitten by the werewolf Justin, Mick elaborates to Sam and Dean that only one out of nine mice survived the treatment and when it was tested on a human, the subject died an agonizing death. With no other options, Sam and Dean attempt to use the cure. Mick tells them they need the live blood of the wolf that bit Claire. As Sam and Dean track the man they believe to be the werewolf, a bartender named Conner, they find that he is human; meanwhile, Justin barges into her hotel room and takes Claire away.
After tracking Justin to his home, Mick is able to stick him with a blood collection tube and is later able to shoot and kill Justin as he fights with Sam and Dean. With the live werewolf blood sample, Mick takes a syringe with the cure and mixes the sire werewolf blood into it and injects Claire. After having the cure administered, Claire begins going through the agonizing process of becoming human again. She appears to die, but soon awakens after her claws and fangs retract and her eyes go back to normal.