To do this, you can use the free iTunes Lyrics Importer application. With iTunes closed, install and run iTunes Lyrics Importer. When you run iTunes Lyrics importer iTunes opens automatically.
You can get lyrics for specific songs by selecting one or more songs and then clicking the button Get Lyrics. Preview the details if you want, then click Update.
You can also update your entire library in a jiffy, without checking every single track. Select the iTunes window, and select all the music by pressing Ctrl-A. In the iTunes Lyrics Importer window, click the checkbox Update Automatically and then click Get Lyrics. The utility will travel through your library, this takes several seconds per song. Click OK when done.
The program stores the lyrics in a music file. To watch and sing, right-click on a track, select Get Info, and choose the Lyrics tab. On an iPod, press the center button repeatedly to scroll to the lyrics screen. On an iPhone or iPod Touch, tap the screen while the song is playing.