Medusa disguises herself as Aunty Em, who owns a roadside curio-shop ("Auntie Em's Garden Gnome Emporium") in the middle of the woods in New York. Percy, Grover, and Annabeth don't recognize her at first because she is completely veiled.
Medusa's face can turn anyone to stone, and that's exactly how she was able to make so many statues which she stories in her front yard and in her warehouse. We later learn that her "artwork" is a hot commodity in the Underworld – Hades displays several of her statues.
Medusa seems to recognize Annabeth right away, fixating on her grey eyes. Annabeth's mother, Athena, has distinctive grey eyes, and Medusa hates Athena. Athena turned her into a monster after catching her getting busy with Poseidon in Athena's sacred temple. Interestingly, Greek mythology tells us that Medusa was killed by a demi-god named Perseus, who was Zeus's son. He chopped off Medusa's head while she was sleeping.