How do I "Minimize" Civ 5 on Windows 7?

Play the game in windowed mode. You can turn this on in the graphical options.

This would allow you to have the game maximised (thus taking up almost all the screen) but make it easy to minimise the game when necessary.

I cannot comment yet, so I have to write this as an answer. The minimize button dissappears after reloading the game, but a workaround for this is to go to Options > Video Options and checking the Fullscreen again, click Apply Resolution to go fullscreen then hit ESC key to cancel fullscreen while the counter is running. Now the minimize button appears again. You have to do this each time you load the game though.