It took me a while to figure out a way of doing this that worked the way I wanted it to. The procedure I've come up with goes something like this:
1. Do an "export as catalog" for all the folders, collections etc you want to move, specifying a path on your external drive.
2. When this has finished, copy the new catalog file back to your main drive, leaving the new copies of all your images where they are.
3. Restart Lightroom using this new catalog.
4. Run a "Render Standard Previews" job, which will generate a new set of previews alongside the new catalog on your main drive.
The result of all this is that you can show and sort your work and organise new collections etc when the external drive is not connected - very useful if you have a laptop, and only need the drive with your image files when you want to edit.
The catalog can reference multiple drives, so you can also import new images straight onto your machine when you are on the road, and then just drag the folders to the external drive from within Lightroom, letting it move image files for you which is always easier than moving them yourself and telling it what you've done later...
Some of this will not be important if you always intend to have your catalog drive with you, but if you use something like a Drobo for safe bulk storage at home you will find it pretty helpful, I think!
Good luck,
Tom