Download and use Gparted to make a partition and format it with ext3 file system. Then follow these steps, do not include anything in between and including the brackets in these commands, those are just quick explanations.
Code:
As root or sudo in single user mode:
1: #mkdir /mnt/newhome
2: #fdisk -l (to find device name of new partition)
3: #mount -t ext3 /dev/???? /mnt/newhome (replace check marks with what is appropriate based on the output of fdisk -l command for the new partition)
4: #cd /home
5: #cp -ax * /mnt/newhome
6: #cd /
7: #rm -fr /home
8: #umount /mnt/newhome
9: #mv /mnt/newhome /home
10: #vim /etc/fstab (edit /etc/fstab with favorite editor if not vim, and add line below with proper /dev/xxxx)
11: /dev/???? /home ext3 defaults 1 2
12: re-boot