How does Medea exercise her supernatural powers and to abet whom?
The use of magic in Medea is a subject of contentious debate in academia. None of the words used by Euripides accurately translate into "magic" or "witch" in the senses in which we use them today. The notion of a witch was not really present in 5th-century BC Athens. Medea is a pharmakis, a woman who deals in love potions, charms, and poisons. But this doesn't make her a witch as we would understand the term.
Much the same could be said of magic. In Medea it's difficult to establish precisely where pharmacy ends and magic begins. We need to bear in mind that, in Euripides's day, the distinction between magic and what we'd now call science was somewhat blurred. Magic could be used to describe natural phenomena of which the ancient Greeks were wholly ignorant, such as thunderstorms.
Yet Medea's powers are undoubtedly considerable and often intersect with the supernatural powers of the gods. When Medea poisons Glauce's golden robe, for example, there is a slight delay before Glauce's limbs are convulsed in burning, agonizing pain. This strongly suggests that Medea's powers have both natural and supernatural elements. The poison works as it is supposed to; this is natural. The delay in the poison's acting, however, only makes sense if there is something of the supernatural in Medea's powers as a pharmakis.
A supernatural element to Medea's power is entirely consistent with her transformation in the play from a woman into a monster. But if she has become a monster, then it is with the tacit approval of Zeus, as the Chorus makes clear at the end:
"Great treasure halls hath Zeus in heaven. / From whence to man strange dooms be given, / Past hope or fear. / And the end men looked for cometh not, / And a path is there where no man thought: / So hath it fallen here."
Medea uses her magical powers even before the actual action of the play begins. In the myth of Jason and the Argonauts, we hear that Jason was able to capture the golden fleece from the dragon that protected because he had magical help from Medea. This magic helped him defeat all of the challenges put before by King Aeetes, Medea's father. She knows that she has betrayed her father and makes Jason promise to take her with him as his wife once he takes the fleece.
Next Medea uses her magic to kill Jason's uncle, and then create a potion that restored his own father's health and youth so that could once again rule his kingdom.
After they are banished to Corinth, things remain calm for many years, but once Jason decides to set aside Medea and their children in order to marry the princess of Corinth, Medea's wrath returns. She promises the use of magic to King Aegues of Athens for him to have children, in exchange for future safe haven. She uses magical poisons to kill and decimate the body of the princess, and she uses magic to produce a flying chariot that whisks her away from Corinth and the wrath of Jason and the King's men who would have her killed as punishment for her crimes.
Medea is a vengeful and dangerous women who should not be tested. She will use whatever skills and knowledge she posseses in order to do what she determines she needs to do.