First, check your Limewire Preferences. Click Player, and make sure you deselect Limewire as your default player. Then go either to your Library or to the Search window and double click your completed MP3 file. If you have iTunes set as your default player (if you don't, open iTunes go to Prferences and set it as your default player) and the song should open iTunes (if not alread opened) and play in iTunes.

You can also go to Home-->Shared and selected all the MP3 files that you've just downloaded and drag them to your open iTunes window---it will automatically put them in the iTunes Library for you. You can then play the songs.