You need to approach her in a private environment. In the begining you can only do this after class (make sure to lock the door or ask her to lock the door). After a while you can get her number and call her over or she may ask you to accompany her to her room after training in the danger room (shes trains there on the weekends).So I got the first after-class scene with Emma, but I don't seem to be able to repeat it or progress at all. Can't flirt with her, can't do sex stuff.
What's the secret?
It takes quite a while to get her to the point were shes comfortable with having your relationship out in the open (not suprising considering shes a teacher and your a student).