I'd suggest to create a partition on the new hdd,
Mount it to some temporary directory.
Then copy all directories from /home over to the
temporary directory that the new hdd is mounted to.
Unmount new hdd.
Edit /etc/fstab, create an entry for
/home that points to the new partition.
See whether everything works fine.
If it does, unmount /home
Delete the files in the old home.
Mount /home again.
P.S.: Check my steps CAREFULLY, I may have
overlooked something, it's been a while that I did
it myself ;) The tips come with the GNU Licenses,
and NO responsibility :D