There's a number of things to consider before you do this:
1. How big are the Events Folders used by the Project in iMovie?
2. Are you using any Photos/Sound clips
The fact is iMovie doesn't keep everything in one single little nice package you can just move around from computer to computer. Everything is split into the Project folder and the Events Folder along with items that might be stored in iPhoto and in iTunes. So getting it ALL in one spot is going to be a challenge.
1. First go to Mac HD > Users > (your home folder) > Movies > iMovie Projects, look for your project name. When you find the folder, hold down the Option key and drag that folder to your DropBox folder
2. Now go to Mac HD > Users > (your home folder) > Movies > iMovie Events. Look for the accompany partner to your Project folder and Option + Drag that folder to the drop box.
3. Try to figure out what if any iPhoto pictures you used or iTunes sound/music clips. You might need to drag copies of those individually into that DropBox folder
So now your friend who wants to edit this iMovie project has to everything you did just now, but in REVERSE order to get it up and running on their Mac. But it's likely going to be a bumpy, bumpy ride.