The key here is to highlight and make use of the differences between mundane skills and true psychic abilities. doppelgreener makes a good point, in that you must ensure the game you're joining includes the capacity for a psychic character.
The skill of Empathy - in Fate Core and in most games - is not in an way paranormal, but a mundane skill some can hone to great effect. Specifically in Fate Core:
Empathy involves knowing and being able to spot changes in a person’s
mood or bearing. It’s basically the emotional Notice skill.
Body language, voice patterns, micro-expressions... these are all things any person can and use - and to some extent abilities we all use.
But a 'psychic' character (and based on how your question is phrased, I'm using Empathic abilities, but as Quentin notes, there are many other 'psychic' abilities possible) will define new ways you can use existing skills. Using Aspects and Stunts, and sometimes spending a Fate Point, you'll take the ability past the simple +2 or reroll. You'll create new abilities. Here's a quick example aspect:
Sometimes I Know More Than I'd Like
This gives you a nicely double-edged Aspect, one which suggests your Empathy skill goes beyond the mundane abilities of others. It gives you a good idea of possible benefits and risks; this can give you great information, but can also be used against you.
Perhaps in play, your ability gives you added insight. Any old PC with Empathy can see the guard is a little sad, maybe. But your connection goes deeper. Perhaps you get flashes that tell you why he's sad. Perhaps you see he's worried about his sick child; now you have something to use to improve your chances of bribing him to let you through.
Here's a related example:
Sometimes I Share My Feelings
Imagine using Empathy in reverse. This is nicely double-edged too. Perhaps you can occasionally make people empathize with you. But sometimes they read you more easily, too. The guard from above might see through your faux sympathy. Or maybe you can nudge his feelings to be less sad, more hopeful, timed with your offer of a bribe, to make him more agreeable to the idea.
Ultimately you have to define your aspects in a way which fits your character but also the setting/premise of the game your joining. These examples hopefully show how its possible to shift Aspects into being a bit more than just a +2 bonus on the skill roll.