To install Linux Mint's Cinnamon desktop on Ubuntu 12.04 you have to add the appropriate ppa first. Open a terminal and enter following commands:
sudo add-apt-repository ppa:gwendal-lebihan-dev/cinnamon-stable
sudo apt-get update
sudo apt-get install cinnamon
To apply Cinnamon, log out of your current desktop session and set Cinnamon as desktop environment on the login screen. Remember that your machine needs graphical 3D support to run Cinnamon correctly.