After having gone through much of the same problem, I found a handful of things that made my life easier. However, as you didn't elaborate as to what steps you took, please accept my apologies if I mention anything you have already done/tried.
First, have you tried to force iTunes to find album art? My memory is a bit stretched here, but I believe you can select all the songs once they are burned to your hard drive, right-click and select something like Find Album Art. I often found this route would locate album art when iTunes didn't download it automatically.
As others have mentioned, one can go to sites like Amazon and assuming the music is for sale there you can usually find a jpg of the album art. You can copy this and then paste it to the album art section in iTunes. However, I have found that the jpgs are often only okay in terms of quality. The same is true of when one Googles for images of the album art.
What I finally wound up doing was something more laborious, but with much, much better results. I would scan the album art, open it in Preview, select ("grab") the album cover (from the rest of the blank pdf file), use the image editing features within Preview to make the image look better (the scanner seemed to desaturate the colours), then save said grabbed and edited image as jpg file to the desktop. I would then move it to the music files. Top quality images compared to most anything I ever found on the Internet. This route does take extra time, but if the album art is important to you I cannot recommend this route highly enough.