Fate operates on a tiered skill system. In order to perform a task you add the appropriate skill ranking to a dice roll, largely the same as in D&D 3.5. The difference is that in FATE you use Fudge Dice (or 1d6 - 1d6 if you prefer), meaning the roll can actually be negative and cause you to operate beneath your 'base' skill. Conflicts of most sort are sets of opposed Skill Rolls, shooting someone pitting your Gun Skill against their Dodge Skill for instance.
Aspects are the portion of the system that sets it apart from standard Fudge. These are phrases, descriptions, or concepts that are embedded in a character or scene. Finding, adding, changing, and removing Aspects is one of the best ways to gain an advantage. Each use of an Aspect allows you to add to a dice roll, or reroll all the dice and take the new result. Generally if an Aspect causes you a problem you gain a Fate Point, while if you use it to help you it costs a Fate Point. Conflict often ends when you manage to put severe enough Aspects on a target to 'take them out'.
Stunts are capabilities that are a bit outside the standard Aspect and Skill portion. These are unique or niche tricks; say being able to reload a gun faster then your Gun Skill would indicate, being really good at seduction rather than just Rapport, or having a really good eye for certain details. Powers are a subset of Stunts in the Dresden Files RPG that tend to be less about skill expansion and deal more with supernatural capabilities. This is where you go when you're looking to make the Hulk, learn to toss around fire, turn into a wolf, or anything that normal people simply can't do. Certain Stunts and Powers require you to spend Fate Points; these are usually things that are too strong to be used constantly.
Fate Points are a measure of how much flexibility a character has. You get a certain number at the start of the game, gaining more as Aspects give you problems, and using them as you alter dice rolls, use certain abilities, or cause small bits of luck to happen.
