To preserve the links between your projects and your events, all moves or copies should be done from within iMovie, (not the Finder). If you do not do this, you may get the dreaded "yellow triangle" which indicates that your iMovie project cannot find your event clips.
Also, if you are a user of Keywords, Favorites, Rejects, or iMovie Date Change feature, I recommend that you use COPY rather than MOVE. COPY seems to preserve your work, while MOVE does not. (Once all is well, you can go back and delete the Projects and Events that you no longer need, after the COPY leaves you with two copies.)
First, the external drive must be formatted as Mac OS Extended (journaled). FAT32 will not work. You can reformat using Disk Utility if you need to.
When importing video from your camera, you can specify your external drive as the target on the import screen.
For existing projects, you should move using these instructions.
There is an error in the instructions where it says to drag the project icon to the icon in the Event Library. You should instead look for your hard drive icon in the Project Library.
You can move events using these instructions.
The above suggestions are great for moving projects and events to an external drive for your personal use. But what if you want to move all the project and event assets to an external drive so you can edit them on another Mac?
If you want to move Events, and copy photos, copy music, etc for editing on another Mac, you should use the FILE/CONSOLIDATE MEDIA feature after moving the Project as above.