Depending on whether you want to install a stable release or an experimental release, you will need to add the appropriate repository to the /etc/apt/sources.list file.

With sudo access, edit /etc/apt/sources.list and add the following line to install the current stable release or current release's source code respectively:

deb http://qgis.org/debian 
trusty main
deb-src http://qgis.org.debian trusty main

Depending on the release version of Ubuntu you are using, you will need to specify the release name as trusty, saucy, or precise. For the latest list of QGIS releases for Ubuntu versions, visit download.qgis.org.

With the appropriate repository added, you can proceed with the QGIS installation by running the following commands:

sudo apt-get update
sudo apt-get install qgis python-qgis

To install the GRASS plugin (recommended), install the optional package by running this command:

sudo apt-get install qgis-plugin-grass

The ubuntugis project installs QGIS and other FOSSGIS packages, such as GRASS on Ubuntu. To install the ubuntugis package, remove the http://qgis.org/debian lines from the /etc/apt/sources.list file, and run the following commands:

sudo apt-get install python-software-properties
sudo add-apt-repository ppa:ubuntugis/ubuntugis-unstable
sudo apt-get update
sudo apt-get install qgis python-qgis qgis-plugin-grass