Would some examples of Aspects people have for various characters help?
The way I'd tend to look at it is to have a couple of things- relationships and personality traits- which pretty much everyone's going to have some of; for example, my Changeling Wizard (Submerged game) has an Aspect for his relationship with his Sidhe father (Daddy Looks Out For Me), and character traits like one I called "I Can Get Some Shining Armour, If You Want."
People are often also going to have Things (Bearer of Amoracchius; Sword Of My Forefathers; My Mother's Silver Pentacle); in general, a lot of these are going to be quite obvious choices (something as significant as a Sword of the Cross is an Aspect...), though it can also be things that are just important to the character; the Sword Of My Forefathers doesn't need to be anything better than a normal sword in mechanical terms if it's a Big Thing to the character. If you're having trouble with character aspects, one option is to think of the sword of Thing that might matter to them, like Harry's silver pentacle.
The other big category I see is things you're character's good at or bad at- Shiro's Peerless Swordsman, for example. These are character-defining skills, and there can be some overlap with the personality traits- that Changeling Wizard I mentioned has Tomes, Not Teachers, 'cause he was raised in pretty much total seclusion by a wizard, so that's doing duty on Knowing Stuff About Magic Stuff, Not Knowing Stuff About Normal People Stuff, and Not Noticing Social Conventions. Again, a lot of these are going to come up from basic ideas about the character- if you want to make a mercenary sharpshooter, you can make that into an Aspect.
The last thing I want to say here is that there's always the option of putting something down that kinda fits, then playing for a while and changing things around if and when character traits that seem aspectworthy come out in play. If you've got a cheerful bodyguard, say, and you discover in play that as well as being protective, you're playing him a bit belligerent and likely to throw himself into fights, you can switch that in as an Aspect (First In, Last Out or something like that).
