First use a great key plugin in whatever editor you are using. One of the best with many options is Keylight - its available in Premier and probably other editors. It allows you to select the key color and then use several methods of refining the key including the usual shrink and grow key controls and alpha channel mods. But is also allows you to change the white and black levels and perform basic foreground color correction as create easy garbage mattes. Once you get used to this plugin (and of course shoot good greenscreen footage) the key part becomes very fast.
Once you have keyed it - just place it over a sold. Find a texture to use as a background and screen it onto the background with opacity to taste. Then use a circular ramp to have some color highlight the keyed action. You can also screen a texture over the foreground with a low opacity and then randomly wiggle it to create a nice "noise" effect. Play around with some other options or plugins but try to be subtle - Dont do too much at a time. With just a little work you can have amazing b-roll cutaways for music videos, promos and any creative pieces.