A couple of pages into the install process you get a choice of three
configurations, the third of which is "specifiy partitions manually" or
something like that. (The others amount to "install Ubuntu next to existing OS"
and "use whole disk for Ubuntu overwriting anything currently on the disk").

So choose the third. You see a table of your existing hard disks and existing
partitions on them. If you want to keep anything that's already there you need
to know which partitions they are, and do nothing to them at this stage.

I'm assuming you're doing a complete fresh install using the whole of one disk.
You still need to take this third "manual" option in order to set up the /home
partition.

Take the option to create a new partition table, which will delete any existing
data or OS currently on the disk.

Create partitions when prompted (or by double clicking on the "free space" in
the table) as follows:
1. about 20GB (at least 10GB) for root. Choose ext4 (or ext3) for the file
system, check the "format" checkbox, and set the mount point to "/"
2. twice the amount of ram you have installed as a swap file. Choose swap file
for the filesystem, and do nothing more with it.
3. the rest of your disk for home. Ext4 or Ext3 filesystem again, and mount
point "/home". This once only -- this once only !! -- format the home partition.

Next time you install (for instance when the next release comes out) do
everything as above except don't format the /home partition. (Take backups
before you start anyway, in case your brain goes occasionally on its own merry
way like mine does and you format it by mistake).

Everything else in the install process is even simpler than that. Have fun!

As for how to use the home partition, all I'd say is don't try and be too
clever, Ubuntu will put everything (Documents, Music, Videos, Downloads, &c.
&c.) in appropriately named folders on /home by default. Took me ages to trust
Windows enough to let it put my stuff in My Documents, and I still don't
completely, but in Ubuntu it's painless, intuitive and pays off when you
reinstall.