OOC:
No, most stunts are just, basically, your powers from you mantle (think template, except more detailed and less customizable). Some are automatic; for instance, as a werecat, I have the Beast Whisperer stunt which states "You inherently understand and may communicate with any animal of the same type as your wereshape [etc.]". No conditions, no requirement, certainly no fate points, I understand and can communicate with cats. On the other hand, it's a rather weak power but hey, it's always on.
Others have a built-in limit to how often you can use them, separate from fate points. So as a criminal, I have "Heat" (as in, heat from the police). I have five boxes, and by crossing them (increasing my heat) I can fuel some of my criminal stunts, and get a +2 to some rolls, or a piece of equipment. Vampires have "Hungry", which fuels (some of) their powers.
Others yet are simply "once per session", and tend to be more powerful, and a very few (and very powerful) require the expenditure of a fate point.
Note: I have two mantles, criminal and wereshifter, because wereshifter is added to a pure mortal mantle. Most characters will have only one.