How big is 'Enormous" ?
I am watching Ben Willmore on CreativeLive this month with a catalog greater that 200,000 images!
I, too, question your definition of enormous.
However, to answer your question:
First backup your old catalog.
In the Library module, select the images to put in the new catalog.
After you verify that the new catalog contains what you want, you can then delete the previously selected files from the old catalog. Do NOT delete the images from the disk drive.
Using multiple catalogs is normally not recommended.
The "safest and easiest way" to split the catalog is to NOT split it at all.
Usually people want to split their catalogs because of speed problems, but large catalogs are almost never the cause of speed problems (Exception: making backups takes longer with large catalogs).
So if that's that problem, tell us exactly what is slow in Lightroom.