To install Mate in Ubuntu 12.04 and 11.10, you need to add its repository to the system. Press CTRL+ALT+F2 to open a terminal, and then execute the following commands: for 12.04:
sudo add-apt-repository "deb http://packages.mate-desktop.org/repo/ubuntu precise main"
for 11.10:
sudo add-apt-repository "deb http://packages.mate-desktop.org/repo/ubuntu oneiric main"
After that, regardless of the version, execute the commands to update the package lists and install Mate:
sudo apt-get update
sudo apt-get install mate-archive-keyring
sudo apt-get update
sudo apt-get install mate-core
sudo apt-get install mate-desktop-environment