I search for the image I want, then download it into My Pictures first. I have Google Toolbar installed with the Picture widget, cycling through My Pictures. So I get a random slide show of all the covers I have downloaded - kind of cool.
After that, it's pretty much what's posted above. I use Download from iTunes first, as it's the fastest way and the image is not stored inside the file. But in many cases, iTunes does not give me the Cover I want. So I have to replace it.
There are three different ways to get the artwork in there. Choose the one you like.
Just be sure it's applied to all tracks - not just the first one of the album. Highlight the track and ensure a picture displays on lower left - use the down arrow to work through all the tracks and check.
Regards,