Here is the step by step procedure. Read carefully before doing any thing :
https://help.ubuntu.com/community/Partitioning/Home/Moving
This guide will follow these 6 basic steps:
Setup your new partition
Backup and edit your fstab to mount the new partition as /media/home (just for the time being) and reboot.
Use rsync to migrate all data from /home into /media/home.
Edit fstab again so the new partition mounts as /home instead of /media/home but not reboot just yet.
Move /home to /old_home and reboot
Delete /old_home.
The guide is written in such a way so that at any point in time if there is a system failure, power outage or random restart that it will not have a negative impact on the system and SHOULD safeguard against the possibility of the user accidentally deleting their home directory in the process.
Please read that web page completely.