If the art is downloaded from iTunes (when you do the get album art process) it's stored in an .itc file in iTunes/Album Art/Downloaded folder. The .itc files are really image files with some header information - unfortunately only iTunes can read those files directly. There's a way of getting the image out, but it needs some Terminal work. I'll let you know how to do that if you want.
If you added album art manually, it's part of the metadata of the file itself. You can extract this for most itunes tracks using AtomicParsley ... but it doesn't always work, especially for mp3s.
if you go to the bottom left of your iTunes window, and click the up arrow, you can view the album artwork. then right click and copy it and paste it somewhere else or drag it to your desktop.