Call of Duty 4: Console usage

To open the console, simply press the tilde key ('~') while you are in-game, this should bring up a minimal console. To get a full console, to see any game output, press Shift + tilde (Shift + '~'). The tilde key is above your tab key, normally.

If nothing happens when you press any of the above key combinations, you don't have the console enabled. To enable it, open CoD4 multiplayer, then go to Options -> Game Options -> Enable Console and switch it to Yes.