Empathy involves knowing and being able to spot changes in a person’s mood or bearing. It’s basically the emotional Notice skill.
Overcome: You don’t really use Empathy to overcome obstacles directly - normally, you find out some information with it, and then use another skill to act. In some cases, though, you might use Empathy like you would Notice, to see if you catch a change in someone’s attitude or intent.
Create an Advantage: You can use Empathy to read a person’s emotional state and get a general sense of who they are, presuming you have some kind of interpersonal contact with them. Most often, you’ll use this to assess the aspects on another character’s sheet, but sometimes you’ll also be able to create new aspects, especially on NPCs. If the target has some reason to be aware that you’re trying to read them, they can defend with Deceive or Rapport. You can also use Empathy to discover what circumstances will allow you to make mental attacks on someone, figuring out their breaking points.
Attack: Empathy can’t really be used in this capacity.
Defend: This is the skill to go to in order to defend against Deceive actions, allowing you to pierce through lies and see through to someone’s true intent. You can also use it to defend against those creating social advantages against you in general.
Special: Empathy is the main skill you use to help others recover from consequences that are mental in nature.