Pat's basically right, with a copy of refinements:
You can move the folders from one disk to another using Finder/Explorer and simply dragging the folder to the new location. Be aware though that by default this will COPY the files, which will become relevant below.
You can also move the catalog folder (the one that contains the .lrcat file and the Preview database) to its new location at the same time.
When you fire up this copied catalog (if you just double-click the .lrcat file Lightroom will start up using that catalog) Lightroom will still be looking for the files in their previous location.
If they're not there, it will still be able to show you the images from its Previews database, but in the Folders view of the Library the folders will show up as red. If you select "Locate Missing Folder" on the top-level folder and point it at the new location of the files, it will try to fix up all the sub-folders at the same time. So it should be a simple process.
However, if it can find the files at their old location you won't get the "Locate Missing Folder" option, so you need to get rid of them. If the disk is an external you could just unmount it, but otherwise you'll probably have to delete the old copy (again, outside Lightroom, using Finder/Explorer). If you just move/rename it that won't necessarily work, as Lightroom does its best to automatically find where the file has been moved to (as long as it hasn't moved to a separate disk).
If you delete the old copy, be sure to empty the Trash/Recycle Bin (or Lightroom can end up finding the copy in the Trash!).
Once the old copy can't be found by Lightroom, it's a simple step to use "Locate Missing Folder" to point it at the new copy, and you'll have preserved the folder structure along with all the catalog details.