Do you mean open a new window at the application level or a new desktop
window in Compiz?

If the former it is done inside the application, usually under File. If the
latter you will need to install the Compiz settings manager. There are two
one is simple and the other is more complex. Once installed they will appear
under System, Preferences. Compiz will not run if you do not have the right
graphics driver installed that supports compositing. You may think that it
is running, but it may not be. You can go to System, Administration,
Hardware drivers to check for a proprietary driver.