There is more than one way to do this. One way is to include the catalog itself on the external drive, and open it from the Mac.
However, you might have the catlog on your internal drive, and the photos on the external, and don't want to move your catalog off of your internal drive. There's another way.
Se my video: A Portable Lightroom Catalog - Mike Hoffman
Remember that in both cases, your drive will be named differently on Windows (a letter) than on Mac (a volume name). You'll need to locate the library folders for Lightroom as you switch back and forth. This is NOT covered in the video above. To address this, you'll want to see this: Lightroom thinks my photos are missing—how do I fix it? - The Lightroom Queen
Or, for more detail: Lightroom: Missing Files, No Longer! - TipSquirrel
This is a simple step if you have all your images under one top level folder.
So, are you telling me my external hard drive that is formatted for use with my Windows 7 PC will be recognized and accessible when plugged into a MAC?
Ah! Right you are. I had totally forgotten it, but I use NTFS for Mac by Paragon Software:
It's $19.99 and works great. You use a standard Windows disk, and it works on the Mac with no problem. Without that, you can read the files, but not write them. You'd get an error if you tried wriing XMP metadata from Lightroom, or opening a catalog on theexternal drive.
Without connecting the external drive at all, you can use my portable solution with Dropbox and Smart Previews. But if you want originals, add the NTFS driver to your Mac and you can share external drives all day between Windows and Mac.