You can point Lightroom's catalog at an alternate file location by:
1. Right clicking the folder, in the Folders panel; and
2. Choosing "Update Folder Location."
In this way, you can bounce back and forth between source images and check to make sure all is working on a second drive, with the ability to go back if you see something amiss. Note that this is always easier if you organize your catalog under one top level folder (thus you only need to update one time).
The method you have shown works well for the files/photos generated in Lightroom. Unfortunately I am a new Lr user, having migrated from Aperture last year. Having used the Aperture to Lr conversion utility I find that the file structure is VERY cumbersome to re-navigate to. For example, I need to navigate to various sub-folders and transfer each photo - it doesn't appear to allow me to link the folders they reside in?
I'm probably doing something wrong but it would take me a month to re-link each photo to its new location on the new hard drive....?
As shown by Michael Hoffman, you re-link the top level folder (in his example, the folder named "Originals") and all folders underneath will also be linked.
You should be able to link a folder, and all the images in that folder will be found. That's why I mentioned top leve folders, if you relink the top level, everything underneath will be reconnected.
Not having used Aperture, nor the conversion tool, I have no idea what the folder structure looks like, unless you can post some screen shots. But again, linking a missong folder) and not an individual image) will reconnect all theimages in that folder and subfolders.
Another option you may consider is giving the volume name of the new drive the sam name as the old drive, so it looks to the OS like the same drive is installed. I know the process for doing this in Windows, but not off the top of my head for Mac. But, if you google "Rename Volume Mac" you'll get plenty of pointers.