First you need to have a mouse cursor. Press F10 to change between mouse look mode and cursor mode.
Then, you need to select the windows to close. Since clicking is also used for switches in the cockpit, if it worked for the windows too we would have accidental mis-clicks.
So, what they did is make single clicks work for the cockpit switches and having alt+clicks work for selecting the windows: just hold down the alt button on your keyboard and left-click on it to select it.
Once you select a window you can then right-click on it and select close, or customize it to display the kind of information you need: all the data about your engine controls, the radio chatter, the flaps and gear messages, the game messages and chat, they are all info windows like that one, they are just customized to show specific information and have transparent background or invisible borders, etc.
All this is covered in the PDF manual that you can find within your installation folder (do read the manual if you haven't, it doesn't cover a lot of things but it sure explains the interface well), as well as in the sticky FAQ thread on the main page of the CoD forum.
Happy flying
