selecting the middle part of a song to add to my movie.

You can do this in your Project, or you can do this in the Clip Trimmer.

The way I do it is to drag in the music clip and drop it on the video frame where I want it to start. The music track should show up as a ribbon underneath the video track. Then, I drag the left "handle" of the music track to the right until it is at the point where I want it to start.

This video from Apple shows this method.

http://www.apple.com/findouthow/movies/imovie08.html#audioclips

I know that I can clip and discard the later part of the tune to suit the length required but how do I chop off some of the beginning if I want to have only a part of the song somewher in the middle of the recording?

You'd have to do it prior to bringing the song file into your Project. You could use Quick Time Pro, Garageband or the free open souce, Audacity.

But by the time you pre-edit your song, you might as well have just done it in iMovie.

If you find yourself using the same bits and pieces of songs in many projects it might be worth the time making the cut-down versions.

Or, if you want to invest the money, Final Cut Pro X allows you to import audio files as events so that you just selcet what you want to add to a project.

Matt