Determine how long your song is. Capture a clip that is at least that long. Put the song on the timeline. Put the clip right above it. Hit the render button and you're done. Or, add some spice by putting fades at the ends of the song.
I won't go into more detail about the AMV since I might be wrong: it might have used two clips. Maybe three.
And, you never know. With the right music and the right video, it might work.
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) I really don't think that there is any sure fire way to faster editing..it all depends on your level of editing experiance, your ideas and so forth.