First, a BIG disclaimer - although I have partitioned many discs, I have
done this precisely ONCE to a disc with an installed system on it and
accept no responsibility for any damage caused to your system; changing
your partitions can cause irrecoverable loss of data and care must be
taken. The best time to do this is during a clean install, but it
*should* work on an already installed system. I also advise you to read
up on the process before you do anything else; the wiki is a good place
to start, especially

https://help.ubuntu.com/community/HowtoPartition

How large you make your partitions is largely up to you - personally, I
have the following

/ 3.00GiB
/usr 4.50GiB
/home 28.76GiB
swap 1.00GiB

the /usr partition is not strictly necessary and could be merged into /
- I do it this way simply so that I can slightly more conveniently
backup my installed programs.

OK, the procedure I used is as follows

1/ Backup /home to DVD or a second hard drive (do NOT skip this step
under ANY circumstances)
2/ Boot from the live CD
3/ System > Administration > Partition Editor
3/ Resize the existing partition (you may need to delete /home from the
hard drive beforehand if space is limited)
4/ Create and format a new partition
5/ Reboot from the hard drive
6/ In a terminal type sudo gedit /etc/fstab
7/ When the file opens, add a line of the form

/dev/sdaX /home ext3
defaults 0 2

obviously changing the 'X' to whatever the system has your new partition
as (you can get this from the partition editor when you create the new
partition - don't worry if it isn't shown as 'sdaX' - it's the 'X'
that's the important bit) and 'ext3' to whatever you have formatted the
partition to
8/ Save the changes to the file and reboot
9/ Copy your backed up /home to the new partition

You should now have /home up and running in a new partition.