In the past having Ubuntu and Linux Mint installed in a dual-boot configuration would have made very little sense to most users. Linux Mint was very similar to Ubuntu and aside from theme choice and a few custom tools there was really nothing to gain by installing Linux Mint side-by-side with Ubuntu. With the release of Ubuntu 11.04 and the release of Unity, their own custom user interface, this is not so cut-and-dry anymore. Many users are not happy with Unity and looking for an alternate distro to meet their everyday computing needs. A lot of users are going with Linux Mint to take "advantage" of the fact it is still using the retro Gnome 2 interface.
This does not mean you are forced to remove Ubuntu from your system. It is rumored that Ubuntu will offer Gnome-Shell as an alternate UI to Unity in their next release so keeping Ubuntu around for a future upgrade is not a bad idea at all. This is very easy to do with a dual-boot configuration and the following guide will walk you through it.
Download the Latest ISO Files
Ubuntu and Linux Mint both offer their own ISO files for download and installation. Even though Linux Mint is based on Ubuntu and uses the Ubuntu repositories there are some significant differences with the ISO files. You can download the latest Ubuntu and Linux Mint releases from their respective websites (please see the References section).
Burn the ISO File
Once the ISO files of each distribution are downloaded you will need to burn them to CD, DVD or USB stick. To burn the ISO image files to CD or DVD on Linux you can use Brasero or K3B, Disk Utility on Mac OS X and on Windows I recommend ImgBurn. If you would rather transfer the image files(s) to USB stick the best way to do this on all three platforms is using Unetbootin which is available for Windows, Linux and Mac OS X. You will need a 700MB or larger optical disk or a 1GB or larger USB stick for each ISO before you get started.
Plan Your Partition Scheme
There are different schools of thought when it comes to partitioning your hard drive when doing multiple Linux distribution installs. Some users like to use a shared directory while others have experienced problems when doing this. Other users, myself included, like to use a dedicated / partition for each distribution containing all Linux directories and then create another partition to hold data such as music, videos, photos and documents to be shared between operating systems. This seems to work well for me, and while you won't be sharing your application profiles, it will give you access to all your multimedia files on both distributions.
A third school of thought, and another that works very well, is to dedicate your main hard drive to your two Linux distributions, allowing the installers to partition as they see fit, and use an external hard drive for all your file storage needs. Regardless of which method of partitioning you choose the only real important factor to consider is that you will want access to your important files on each operating system. As long as this happens you really can't go wrong.
Install the Distributions
One of the major developments for Linux distributions over the past 10 years has been how easy they have become to install. There really is nothing to installing a Linux distribution now aside from booting the LiveCD, hitting next a few times, entering a username and password, hitting next a few more times and waiting.
One consideration you do have when installing multiple Linux operating systems is which distributions boot-loader you want to use. A minor issue I know but not all boot-loader themes are created equal! In this case I would recommend installing Linux Mint first allotting half your hard drive space to the install and then running through the Ubuntu install choosing the "Install them side-by-side" as your partitioning scheme from the Ubuntu installer. This will take care of all the needed partitioning for you (in this assumption you are using an external drive to hold your multimedia files) and now all you have to do is wait for the install to complete.
Reboot and Rejoice
After your Ubuntu install the last step will be to remove the LiveCD media and reboot. You will then be greeted by the Ubuntu boot-loader and given the option to boot either Linux Mint or Ubuntu. congratulations, you are now dual-booting and ready for any further developments on both the Ubuntu and Linux Mint fronts.