Powers
A Power is an ability you have that sets you apart, an ability that the average person just can't duplicate. It might be supernatural, or it might just be the result of years of training. Whatever it is, it's what has allowed you to survive for as long as you have. You have one Power. Each use of a Power costs one Fate Point. More impressive uses of a Power may cost multiple Fate Points.
Some sample Powers:
Sorcery
The Sorcery power allows you to take the Magic skill (players are encouraged to rename this power to suit their character's background).
Badass Normal
You don't have any powers. You're not a wizard, you can't bend spoons, and you don't turn purple when Mars is in retrograde, or any of that crap. But what you do, you're damned good at. Pick two skills. By spending a Fate Point, you can get a +3 bonus for a single roll in either of those skills.
Sands of Time
You have a limited degree of control over the flow of time. At the cost of a Fate point, you can rewind time just enough to retry a roll, or to force an ally or enemy to reroll their own!
Faith
This must be related to one of your Aspects (Man of the Cloth, Daughter of the Goddess, Freedom Isn't Free). You have strong faith in something beyond yourself. It may be religious, or a political ideal. Whatever it is, it gives you great mental fortitude. Gain the Conviction skill. The Conviction skill can be rolled instead of Mental Defense (though mental defense still takes the hit in the case of a failed roll). In addition, you add +3 to a skill when invoking your related concept instead of +2.
Defensive Adaptation
Perhaps you have armor plated skin. Perhaps your flesh is coated in a thin layer of spikes. Perhaps the wind itself defends you. One way or another, you gain the ability to cancel a lost defensive roll in exchange for a Fate point.
Offensive Adaptation
Maybe your teeth are fangs, or your nails are claws. Maybe your fists are hammers. Hell, maybe you can shoot laser eye beams. Your Power will give you the ability to take points from your opponent's physical defense with a single attack roll, but you'll have to spend a Fate point.
Psychometry
You can read the history of an object. By touching an object, you can read information from the object, from the emotional state of the last person to use it to its history for the past ten years. Gaining any useful, concrete information from this torrent of images and emotions costs one Fate Point. Alternately, you can gain a +2 bonus in a skill in which you have fewer than three dice. If you have more than three dice, there's nothing more the object can teach you. This also costs one Fate Point.
Aspects
An Aspect is a statement or phrase that defines your character. Maybe it's a personality quirk. Maybe it's their physique. Maybe it's their job. Whatever it is, it's something that has a major effect on them and what they do. An Aspect is used in one of two ways. Tagging an Aspect costs a Fate Point. To tag an Aspect, that Aspect must relate in some way to the task at hand. Once an Aspect is tagged, it gives a bonus to whatever skill a character is using. Either it lets a character reroll after a failed attempt, or else it gives them a +2 bonus to the final result. However, an Aspect is not always beneficial. Sometimes, it can be detrimental to your current task. When that happens, the GM (or one of the players) might Compel the Aspect. Compelling an Aspect adds a new complication to the scenario. It may increase the DCs needed to complete the task or restrict the skills characters can use. However, when a character's Aspect is Compelled, it gives them another Fate Point to spend. A player may refuse the Compel by spending a Fate Point, but this gets costly fast. Each character starts with three Aspects.
Scenes (and NPCs) can also have Aspects. For example, a chase through a sewer might have the Aspects Dark and Nasty, Rats in the Walls, and Something Moved, while the pursuers might have the Aspect Paranoid. If the players guess the Aspects for the scene and the NPCs, they can tag them to their advantage, just like they can tag their own Aspects
Sample Aspects:
To Serve and Protect
You're a cop, sworn to protect civilians from the line of fire. You've got training that can help you, but it also puts limits on the things you're willing to do.
Stubborn as a Mule
Once you get set on a course of action, it's hard to sway you.
Man of Iron
You're tough as hell. You can keep going after taking damage that would fell a lesser man.
[Insert Guild here]'s Most Wanted
The __ know your face and wants to put you down. You are often subject to persecution and harassment by members of the _.
Shadow Market Buyer
You've got contacts in the less savory parts of Ravnica.
Academia Nut
You work at a university, and have the resources and responsibilities therein.
Fate Points
Fate Points represent a character's ability to go beyond the norm, to do incredible or near-impossible feats, as well as random coincidences that crop up for the characters. They're used for Powers, Aspects, and Making Declarations. A character begins a Scene with three Fate Points, and can gain more by having their Aspects Compelled. When a new scene starts, a character's Fate Points reset to three.
The use of a Power generally costs one Fate Point, though a DM may require the use of multiple Fate Points when using a Power in extraordinary ways.
Tagging an Aspect always costs one Fate Point (though more than one Aspect might be Tagged at a time).
A Fate Point can also be Make a Declaration in a Scene. Typically these are fairly small, governed by coincidence. For example, a player might need to justify why his character happened to bring along a book on Mesopotamian artwork on a trip to Iceland. If he spends a Fate Point, he just happened to be doing some light reading. Alternately, a character might be trying to get in on a scene. If he spends a Fate Point, his character can happen to be at the right place at the right time. All such uses of Fate Points are subject to GM approval. "The ape-men's creator suddenly drops dead of a heart attack" is almost certainly not going to be approved. However, "The ape-men are deathly afraid of fire" might be. In general, if it makes the scene cooler and more fun for the entire group, it's more likely to be accepted.