Another way is to do it in iMovie. After dragging the full track into iMovie, simply drag the ends in to shorten the track to the section you want. Then reposition (by dragging) that section to the appropriate spot in your movie.
Just to be clear - when you drag a song into iMovie, drop it onto a thumbnail (not the background) near the position you wish it to play. A green coloured bar will appear just below the thumbnails. This bar can be manipulated as described above.
If you wish to fine tune, use the Clip Trimmer. Access this by clicking on the small gear icon at the beginning of the track. In the panel that opens select "Clip Trimmer" - a window opens showing the waveforms for the audio track. You can drag the yellow handles to highlight/select the piece you want to play. As you do this, you can view the associated video clip in the viewer at the top right of your screen.
John