When do Romeo and Juliet find out that they are members of the enemy families? Who tells them?

Romeo and Juliet each find out who the other is at the end of Act I, Scene 5.  This is the scene where the Capulets hold a dance and Romeo and Juliet first see each other.

Both Romeo and Juliet learn of the other's identity from the nurse.  The nurse comes and tells Juliet her mother is looking for her.  Romeo asks the nurse who Juliet's mom is and the nurse tells him.

Then, after Romeo has gone, Juliet asks her who Romeo was.  The nurse tells her.  Both Romeo and Juliet are unhappy, but still in love with each other.