Select the "Sequence" in your "Browser" window. Open the "Media Manager". Select "Copy" and selecte the "Delete unused media from duplicated items" option. "Delete unused media,..." option means it will copy only what you used. There is also an option for handles "Use Handles xx:xx:xx:xx" that lets you copy only the media you want, plus some time before and after your clip for handles.
What copy does is it makes a complete copy of your project with the option to only copy the media you used, to a different drive, or anywhere you need. It does work,.. I use it all the time and have done so for years!
Like Shane said, read up on it,... it's pretty easy, and don't let people tell you it doesn't work on Final Cut Pro,... I've been using it since FCP 1.2.5 without any problems!!!! (FCP 1.2.5 did have some problems,... but current FCP versions,... at least since FCP3, don't have any problems!).