Right click the song in iTunes and choose Get Info. Second from the right is the section "Lyrics" where you can paste the lyrics of the song. The lyrics will show up on top of the album art when the song is played on the iPod. Tap the album art to show it if you don't have all the controls visible.
I’m not sure how long it has been there, but the last three or more versions of Music/iTunes have lyrics display built in. When a song is playing, if it has lyrics installed, the lyric icon will be highlighted. Tap it, and the lyrics appear. When the next song starts, the lyrics will automatically change, too. Unfortunately, they don’t automatically scroll.
Best Answer
There's no built-in functionality to download lyrics in iTunes, but there's a slew of software designed for this purpose:
Windows:
OS X: