Changing the background color of the sidebar in Mystique may take a little work. Here is a basic example to illustrate:

#sidebar {
	background-color: yellow;
}

You can try it out by adding it to your Appearance → Custom Design → CSS editor and clicking the Preview button.

Change the color name to a color code of your choice:
http://automattic.github.com/Iris/

If you make the change, note that the sidebar area is a block that may stop short when the main content area has a lot of content in it. Try adding a test post with a lot of content to see what I mean.

Also, this is another good resource you can check out if you are starting out with CSS:
http://www.htmldog.com/guides/cssbeginner/

And this:
http://en.support.wordpress.com/custom-design/editing-css/

Thanks for any help.