The iPod is specifically setup to read the file data it gets from iTunes - even if you didn't get your tracks from iTunes, you still need the data from it so the iPod knows how to organize them.
Let's say I have Brandi Carlile's track "The Story" as an MP3, but the iPod doesn't know anything beyond the file name. First, I open iTunes and select Library - Music, so there's all my tracks displayed, including The Story. I select that, and then right-click on it and click Get Info; this displays all the iPod info attached to the song (if you didn't get the track from iTunes then most of this will be blank). Then select the Info tab - this is where all the inputtable info fields are.
*The only really important fields that you have to have filled in in the Info tab are the Name, Artist, and Album fields.* To do this correctly, find the track or album you're inputting info for in the iTunes store - I search for Brandi Carlile, her results come up so I know I have the spelling correct, then I find The Story - it turns out that the album it's on is also called The Story. So there's my three fields filled in, I click Okay and that's it, my iPod now correctly has this track listed within it's own album. You can also go back and fill in the other relevant organizational data as you need (if you like organizing by genre, go ahead and fill that in.)
If you do this correctly, you can then right-click on the track with your completed info and select Get Album Artwork; iTunes will automatically download the cover artwork and apply it to your album for playback and Cover Flow viewing. (If it doesn't work, this usually means something is mispelled/doesn't match the iTunes Store info, or your iTunes needs to be updated.)