Fate Core
Aspects
Aspects: brief phrases that define and describe people, places, and things.
Example: The characters come across a tavern that Stanford decides to duck into for a drink and to search for someone the party is looking for. Avi describes the place quickly, mentioning that it is Crowded.
Invoke: to use an aspect to create a positive (for you) effect on the story, either by boosting a roll, triggering a reroll, or asserting something about a scene.
Example: Stanford is alone at the bar of a tavern that Avi has described previously as Crowded, when he gets into an altercation with a few tough looking guys. Unable to see his companions, Stanford attempts to lose them in the crowd. Chris Mu. rolls Stanford's Stealth, with a net result of +2. Wanting to guarantee that he succeeds on the roll, Chris invokes the Crowded aspect of the bar, spending a Fate Point to add +2 to the roll, for a total of +4. Stanford quickly makes his way out of the bar, leaving his pursuers behind.
Compel: when the GM invokes an aspect to complicate a player character's life, either granting one Fate Point if the compel is accepted, or costing one Fate Point to negate.
Example: Jeroy has a tendency to act without thinking, especially in the throws of a barbarian rage. As the party attempts to make its way into a cave full of pirates, the others successfully subdue a pair of lookouts stationed near a large bell, the bell having been rendered Silent by magic. Avi decides to compel Jeroy's aspect Smash First, Ask Questions Later to assert that Jeroy would do something here that complicates things for the party. Chris C. accepts the Fate Point and says that Jeroy decides to smash the bell despite it being silenced, in full view of another group of pirates farther in, who manage to sound the alarm.
Aspects are one of the defining features of Fate. Virtually everything of note in the game will have one or more associated Aspects. From a storytelling perspective, these function as quick, descriptive tags that sum up and differentiate characters, objects, and even scenes. These are not standardized, and can come in varying degrees of specificity. A tavern scene might simply be Crowded, or it might be Full of Music and Chatter. Aside from the obvious storytelling differences to these two aspects, they can have different mechanical effects. Aspects do not need to be exhaustive, and not everything needs an aspect. A group of nameless NPCs harassing the player characters may all fall under the aspect Angry Mob rather than being handled as individuals. A character's armor might simply exist without an associated aspect, while their heirloom sword, passed down in their family through a century of martial tradition, might have the aspect Century of Nicks and Sharpenings.
Mechanically, aspects are used by players and the GM for a number of purposes. The most typical use of aspects is for invokes. When a player or the GM invokes an aspect, they (generally at the cost of a Fate Point) are asserting that the particular aspect allows them to influence the scene. A character trying to lose themselves from pursuit into a busy tavern could invoke the tavern's Crowded aspect to boost a Stealth roll, or allow for a reroll of a low Stealth roll to achieve success. The GM could similarly invoke the tavern's Full of Music and Chatter to boost an NPC's own Stealth roll, asserting that the noise of the scene makes it harder for a player character to use Notice to listen in on a conversation.
Another use of aspects is through compels. These are typically used by the GM to create complications in the story as a result of aspects the players have. Accepting a compel grants a Fate Point to the player being compelled, while ignoring or negating a compel costs a Fate Point. As a means of heightening the dramatic tension or complicating the story, and as the primary method of acquiring Fate Points, players are encouraged to seek out compels and situations where their character's aspects might make life harder, though the ultimate decision on what counts as a compel is up to the GM.
Character Creation
The sections below list out the steps of creating a new character in Fate Core.
High Concept
High Concept: A brief phrase that sums up who a character is, and what, from the broadest picture, they might be capable of.
Example: D decides to make a spell slinger, who gets his powers from a pact with something dark and terrible. Because everyone's making "good" characters, he decides that his arrangement with dark powers is unintentional, something that will likely end up being the focus of his Trouble. He creates the High Concept Warlock of ...Taiia? and moves on.
When creating a character, it can be useful to start by writing out a brief sentence, or a few sentences, describing who the character is. From there, condense the description down into a brief phrase.
Trouble
Trouble: a personal struggle or problematic relationship that complicates a character's life.
Example: D already has an idea for his Trouble, since it links pretty closely to his High Concept. Since it's something that's going to be compelled against him, he creates the Trouble Unwittingly Serving the Great Old Ones, and anticipates this is going to make life VERY interesting.
A character's Trouble aspect is the main thing that complicates their life. It's generally not something that is easy to resolve, as if it was they would've done so by now, but nor is it something that should paralyze the character and prevent them from engaging in the story. This doesn't necessarily have to tie directly into the High Concept. A character whose High Concept is Scholar of the Arcane Arts could have the unrelated Trouble Egomaniac, something that can still be compelled frequently.
Note that good Troubles have a silver lining to them. D could invoke Unwittingly Serving the Great Old Ones if a situation arose where could identify signs of their presence, something he would be familiar with. A character with Egomaniac could argue an invoke for resisting compulsions due to their high sense of self.
The Phase Trio
The final three aspects created during character creation relate to a characters first foray into a life of adventure, and their interpersonal interactions with the other player characters prior to the start of the game.