The center of the fog is the player, of course! And then you just have the start and end distances.
I'm not talking about entities, I'm talking about extending the existing fog (with Cubescript variables). (I said that in my other post, but I guess it wasn't prominent enough.)
If you wanted to do localized fog, though, you probably would want to use an entity. An area particle effect would probably work fine. Take a partially transparent (~20%?) round smoke ball image and render a bunch over an area. Rotate the images and fade in and out. Maybe move around (on XY axes, maybe a little Z) too.
You could even drop the world fog way down while you're inside, to really limit visibility. (Hey, do I smell smoke grenades? :D) But that is getting a little complicated.
Anyway, Windecker is right. You should probably split this off into its own thread.