Important update: The Ubuntu Phone project was discontinued in April 2017 and is no longer being worked on.
The mobile version of the popular Ubuntu operating system.
Find out more about it on the official website.
There are two ways of installing Ubuntu on your Nexus 4: Single or dual boot. Dual boot is definitely easier (that irony!).
Single boot requires you to have a desktop PC with Ubuntu installed while dual boot can be achieved by downloading an app from Google Play.
The single boot instructions are presented very well on the official Ubuntu developer site: Installing Ubuntu for devices
Advantage: Very easy to reflash without losing your data
Disadvantage: Requires a PC with Ubuntu installed
Dual boot can be set up by downloading MultiROM Manager from Google Play, installing the MultiROM parts from inside the app and then installing Ubuntu from inside the app as well.
Advantage: Very easy to get Ubuntu working without the need of a PC
Disadvantage: No way to reflash later without losing your data (but don't worry, updates work fine)
No matter which installation method you choose, you will be presented with a list of channels to pick from, each of them containing different versions of the OS.
If you want stable images with updates once every six weeks, choose the channel "ubuntu-touch/stable".
Daily development builds can be installed from the "rc-proposed" channel, but this is not to be recommended as they break regularly (sometimes they do not even boot).
Note that in that case there is no way to recover your data if you are using MultiROM.
Official promotion videos: