Supreme Commander is an old game and wasn't designed to run on windows 7 or 8 so if you install it you will likely get an error (something about Supreme Commander has stopped working)
Don't panic, it's easy to get Supreme Commander running on Windows 7 or 8 using windiws XP compatibility mode.
To make Supreme Commander run in XP mode you need to find the game file (called an executable or ".exe") and change it's properties:
Step 1: Find the Supreme Commander Executable:
Navagate to c: using windows and in the top right corner of the window there is a search box. Type in "supreme" and press enter. Before long, the Supreme Comander application file will appear. right click on "SupremeCommander" and click properties (not the icon with the arrow, that's a shortcut).
(sorry windows is in Spanish on the screenshots)
Step 2: Instruct windows 7 or Windows 8 to run the game in compatiblity mode:
With the Supreme Commander properties tab open, look at the tabs at the top, click "compatiblity" and then click to put a check next to "Start this program in compatability mode" and choose: Windows XP (service pack 3).
Supreme Commander will now run on Windows 7 or 8. If it does not, try compatibilty mode Windows XP (service pack 2)