Alternatively, make a directory called /home on your new hard drive (you may have to use gparted or fdisk to make an ext3 partition first and mkfs.ext3 to format it).
mount /dev/xxx1 /mnt/temp-mount
cp -R /home/youruser /mnt/temp-mount/home/
chown -R youruser.yourgroup /mnt/temp-mount/home/youruser
Edit fstab and change the /home line so the first part points to /dev/xx1 where xxx = the dev id for the new drive (hda etc) and the 1 represents the partition.
LABEL=/home /home ext3 defaults 1 2
/dev/xxx1 /home ext3 defaults 1 2
Then reboot and make sure it works.
Now you can delete the /home partition (or the data in home if it is part of /) on your 80gb and free up the space for /usr to use.
So you need 2 partitions, one for /home and one for /u01.
Use gparted to make them. I'd recommend 280-300GB for /home, and whats left should be more than adequate for a lot of databases. They should become hdx1 and hdx2.