Which version of Aperture? In 3 you can only trim audion if it is the scondary audio track.
When you mouse over the secondary audio track the cursor turns into a hand. Click the secondary track it will be selected (outlined) now place the hand at either end of the clip it will chnage into a duple arrow now drag the clip to adjust the length
The trim button is only available, if you view your Audio in the Viewer, not when you are editing a slideshow, as the paragraph in the manual says, that Frank pointed to - I think you may be referring to this paragraph of the help:
But while you are editing a slideshow the trim button is not available, and you can only trim the end of the clip and shorten it this way.
You will have to trim the audio you have imported to Aperture in the Viewer, befor using it with your slideshow, or to set the start time in iTunes, if you are using audio from your iTunes library - in iTunes you can set the start time in the song Info Panel - in the "Options" tab.