if the GPS is enabled, but the app doesn't use it, does it drain battery? (I understand that GPS drains battery because it requires a different component to be charged up.) Or the fact that the GPS is enabled only means that the App can use it?
When you give an app permission to use your location, in other words enable GPS for it, the app may or may not use it. Some apps use it briefly to get a fix once each time you start the app, some apps don't use it until you perform a certain action in them, others use it whenever the app is open, and some even continue to use it after you've closed the app - for instance if you're doing turn-by-turn directions in the background.
To know if an app is actively using the GPS, and thus draining the battery faster than normal, is to look in the status bar next to the clock. If there's a little white arrow, then an app (probably the one you've got open right now) is actively using the GPS.
If you don't have an app open, and the arrow appears, you can find out which app is using the GPS by going to the
Settings app, selecting
Location Services and going down the list of apps. For each app there's the app name, and then a selector that determines whether that app is allowed to use the GPS. Scroll down that list and look for a little arrow between the app and the selector. If any app is using the GPS right now, it will show up as an arrow next to the app name. The color and fill of the arrow provide additional information, which you can find out about here: How can I tell when the iPhone is actively using GPS versus only using region monitoring? . That question also gives a screeshot of the
Location Services screen with an arrow showing, so you can get an idea of what to look for when you go through your list of apps. It's for the iPad, but the iPhone is very similar in design.
If an app is using GPS and you don't want it to, change the selector to
OFF and it will stop using the GPS and draining your battery.
If GPS is enabled at an app level it doesn't use more battery unless an app uses GPS. And even if an app uses GPS it can do so in a way that minimizes it's usage and battery drain. For example if Foursquare were to use GPS efficiently it would only fetch your location when you are checking in or looking up places to check in then turn off it's access to the GPS.
Now at a system level enabling GPS might drain the battery a little but that depends on what you have enabled, i.e. Find my iPhone.