How do I install drivers for an Intel HD Graphics?

The Intel cards are automatically detected and installed in Ubuntu, no need to install further drivers. See this question if you want them to be recognised in System Info.

However, if you feel that you want to install a more recent driver (I dont recommend this if you do not know how to recover from a broken graphics driver) you can add the xorg-edgers fresh X crack PPA and update your system with the packages from there.

To do that open a terminal and use these commands

sudo add-apt-repository ppa:xorg-edgers/ppa
sudo apt-get update && sudo apt-get upgrade

Reboot with

sudo reboot

Again, do this only this with extra caution!

If you don't want the bleeding edge in drivers, you can also use the x-swat PPA, which contains more stable drives.

sudo apt-add-repository ppa:ubuntu-x-swat/updates
sudo apt-get update && sudo apt-get upgrade

The Intel Graphics Update Tool for Linux^(*) allows you to easily install the latest graphics and video drivers for your Intel graphics hardware. This allows you to stay current with the latest enhancements, optimizations, and fixes to the Intel Graphics Stack to ensure the best user experience with your Intel graphics hardware. The Intel Graphics Update Tool for Linux was available for the latest LTS version of Ubuntu at the time this answer was posted.

Thanks to Shahe Tajiryan.

^(*): Intel Graphics Update Tool for Linux is discontinued