You can use them in a number of ways.
The most straightforward is to upgrade your own skill check once (turns one Ability(green) die in your pool into a Proficiency(yellow) die, if you do not have any Ability dice in your pool then using a Story Point would add an additional Ability dice to the pool) or you can also use it to increase the difficulty of an opponents check (turns one Difficulty(purple) die into a Challenge(red) die and again if your check does not contain any Difficulty dice it will instead add one to the check).
Certain Talents and abilities will require the use of a Story Point to activate, these will be noted in the relevant description.
You can also use a Story Point to inject narrative changes into the story. For example if you were trying to find a way into a building you could use a Story Point to state there is a handy vent somewhere, or that the guard on patrol has dropped their access card, or that you know the guard so have a possible in to negotiate with them. This isn't a god-mode option though (for example you can't spend a Story Point and just declare the big bad drops dead from a heart attack) it's more for slight narrative tweaks.
The GM points are used in a very similar manner.