It is a two step process. First, you have to pick the "Set featured image" link usually found on the bottom right of the Edit Page / Edit Post page. That brings up the Media Library menu. You then select an image from there (think it needs to correspond to the theme image size, e.g. 940x180 for Twenty Ten). Then when you pick the "Show" option for an image, one of the options at the bottom of the image info pane is: "Use as Featured Image". Pick that, and that image will be used for the page/post. Kind of non-obvious path, I think.
Don't know about changing the background for each page, however.