I think I just graduated from newbie-ville.
I successfully partitioned the free space (using cfdisk), set up my file system (mkfs.ext3), and moved my /home directory to the new partition using this great command from MaroonBaboon
# cd /home ; tar cf - * | ( cd /mnt/newhome ; tar xvf - )
BTW - I made a small variation on the whole move thing which worked quite nicely.
1) I copied /home to /mnt/newhome, edited fstab appropriately, and testing that this worked by mounting and unmounting.
2) I created a dummy directory called /home/test. Remember I previously copied /home to /mnt/newhome without the dummy "test" directory
3) I edited fstab to mount the new partition at /home. And then mounted the new partition.
4) If the mount worked properly and all was well I should no longer see /home/test. And this is exactly what happened (fortuitously). I could then umount and see the /home/test directory reappear.
5) Finally I reboot and start working on the new partition. Assuming all goes well for the next couple of weeks I'll unmount the new partition and delete the old /home (I know I could probably do this now, but I'm a chickenS&!t).
Oh yeah -- I also rearranged the desktop on the old home just to make doubly sure when I rebooted.
A couple things that might help other newbies with similar problems. First, cfdisk doesn't come installed on RH9 machines - you have to go out and download the cfdisk rpm (I used cfdisk-glibc).
Second, I wasn't able to access these commands from a terminal inside X - even as SU. I had to open a new shell using ctrl-alt-F1 then login as root to use fdisk and/or cfdisk.
Third, the documentation on cfdisk is a little sketchy. It wasn't clear that you have to Write the partition after you set it up - and doing this the first time is a little scary if you're not 100% positive that this is the proper thing to do (I was probably 95%).
That's all. Thanks Scruff and Trickykid. I really appreciate all your help!