First thing is to make sure that you have both installation medias, and that your system is set to boot from CD. If you don't download 12.04LTS and 10.04

As far as installation goes, I would recommend that you install 10.04 first, just so 10.04's older grub version won't replace 12.04's newer version.

As far as sharing goes, read below:

The only two partitions that it is really safe to share are /home and
swap. Swap data is temporary anyway and not expected to survive
between reboots, so a common swap partition makes a lot of sense.
Running a separate home partition is a good idea, because your data
survives reinstallation, but it can be a little tricky to share /home
between two distros. Because of differences in program versions, and
possible conflicts of user IDs, it's not a good idea to share a home
directory between two distros, so you're better off using one home
partition but a different home directory on that partition for each
distro.

You can either use a different username with each distro, or use the
same name but a different directory. The convention of using
/home/username as the home directory is just that, and is only a
default setting, not a requirement. If your username is bryan, you
could have home directories of /home/bryan-ubuntu, /home/bryan-studio
and so on. Each distro installation is a separate entity: you cannot
share installed program and library files between two. Some distros
modify programs to suit their own needs, and it is very rare for them
to update versions at exactly the same time.

You could share /boot in theory, but it can be a lot of work to set up
and maintain, and a separate /boot partition is not really necessary
with modern hardware. Using the number of partitions per distro that
you are using is sure to exceed the partition limits of the system
before long. You have a couple of options here. The simplest is to
have a single root partition for each distro, plus common swap and
home partitions. Each distro is then a self-contained entity within
its own partition. A more flexible option, especially if you want to
run multiple distros, is to use the Logical Volume Manager (LVM). This
would entail having a small /boot partition for each distro plus a
large partition given over to LVM. This would then contain logical
'partitions' for the various distros, as well as /home and swap.

The advantage of this approach is flexibility, volumes can be created,
resized and removed on the fly, which is useful when experimenting.
Many distros have an option to use LVM during installation. There is
another option when experimenting with different distros:
virtualisation. You can install VirtualBox on Ubuntu and create
virtual machines within that for any distros you would like to
experiment with. Only when one convinces you that you want to use it
long term do you need to worry about partitioning the disk to install
it.

Source: http://www.tuxradar.com/answers/589