Google up some lyrics. The simplest way to find lyrics online is to google for them. Just be aware that certain lyrics sites contain malware. If Google warns you away from a particular site, you might consider taking its advise.
Paste the lyrics into iTunes. Select the song you want to add lyrics to in iTunes and choose File -> Get Info or Right-click (ctrl-click) Get Info. Select the Lyrics tab from the window that opens and paste the lyrics into the provided text field. Click OK to dismiss the window and save your lyrics.
Repeat. Add lyrics to as many songs as you want--just be aware that the process is a bit tedious so you might not want to do your entire library at once. (You might also want to check out the PearLyrics dashboard widget to automate the process.)
Sync. Connect your iPod to your computer and syncronize it to your iTunes library. The lyrics will sync along with your songs.
Play. After syncing and removing your iPod, select any song you've added lyrics to. To view the lyrics, press the Center ("OK") button to cycle between the normal playback screen ("Play status"), the playback scrubber, album art (if available for your track), the lyrics screen (if you've added lyrics), and the star rating for the track.
Take note. As this Apple support page points out, only some music file types (AAC and MP3) supports lyrics. Others (like WAV and QuickTime files) do not.