From my experience and reading, it doesn't seem like many "spontaneous" plays are made up during the course of a game, at least in most situations. A coach sits down with his playbook, and film of the other team, and narrows his playlist down to a certain number of plays he thinks will work against said team. He then sits down with his Quarterback and various coaches and goes through what they think will work, and narrow the list down further.
Now obviously there are going to be variations of plays called, like the same play can be run from any set(ie: single back set, i formation, spread, etc.) and there will also be variations on the actual plays, like a WR going right instead of left on a given play depending on the tendency of the other teams defense, etc.
A coaches gameplan is very particular and they usually hash out everything before the game, as it'd be tough to just draw up a random play and have all the players understand it and make it work on the fly. The play's the coach draws up for any given game are usually run quite a bit in practice the week before the game.
Here is a small article that kind of explains what goes into planning for a particular game. Doesn't say anything about making plays up on the fly, but it will give you specifics on what goes on during gameplanning in general.