These instrutions show you how to get GNU/Linux with the MATE Desktop installed on a Raspberry Pi using Arch Linux Arm. Arch Linux Arm is a distribution of Linux for ARM computers that can be installed as an alternative to raspbian, which usually comes pre-installed on a raspberry Pi SD Cards. This is a lighweight, up to date and rolling distribution, read on if you want to try it out.
To get started, navigate to the install instructions for your Pi on the Arch Linux Arm website. These instructions tell you how to set up partitions, install the base operating system and where to download the base Arch Linux image from. These instructions assume that you have access to a linux desktop or laptop computer and are all linux commands.
For Raspberry Pi 1, B and model B+ models, follow the the ARMv6 instructions. If you have a Raspberry Pi 2, follow the ARMv7 ones.
After completing the install instructions put the SD Card into your Pi, boot up and log in as root, you will find the root password at the end of the install instructions.
As root, perform a system wide update with the command:
# pacman -SyuOnce done, install mate desktop and the lightdm window manager:
# pacman -S xorg xf86-video-fbdev mate mate-extra lightdm lightdm-gtk-greeter
and configure lightdm to autostart on bootup, this will make the Pi autostart a graphical user interface:
# systemctl enable lightdm
Finally change the default passwords for the alarm and root users. As root and issue the following commands from a command prompt
# passwd alarm # passwd root
An optional extra configuration would be to enable autologin. You can get instructions for doing this from the arch wiki here.
You now have a bleeding edge rolling distribution on your raspberry Pi. For further reading and information on using Arch, the arch linux wiki is an excellent source of information