1. First, check the software sources, then paste this command into the terminal:
sudo apt-get install build-essential cdbs dh-make dkms execstack dh-modaliases fakeroot
  1. If you have a 64 bit system, do this step:
sudo apt-get install ia32-libs-multiarch:i386 lib32gcc1 libc6-i386
cd /usr
sudo ln -svT lib /usr/lib64
  1. Paste these commands into the terminal to create a new folder and download your driver:
cd ~/
mkdir catalyst12.4
cd catalyst12.4/
wget http://www2.ati.com/drivers/linux/amd-driver-installer-12-4-x86.x86_64.run
chmod +x amd-driver-installer-12-4-x86.x86_64.run

4-A) IF you have Intel HD graphics AND discrete ATI GPU, then do this(and reboot):

sudo ./amd-driver-installer-12-4-x86.x86_64.run

4-B) IF you have just the ATI Graphics card, then do this (like in video), it WILL take a while:

sh amd-driver-installer-12-4-x86.x86_64.run --buildpkg Ubuntu/precise
sudo dpkg -i fglrx*.deb

5)Overwrite the /etc/X11/xorg.conf file(anyway):

sudo amdconfig --initial -f
  1. Force the use of the new xorg.conf file:
sudo amdconfig --input=/etc/X11/xorg.conf --tls=1

7)Reboot the computer, to verify your installation, follow the 8th step, otherwise you’re Done.

  1. To verify your installation, in terminal type:
fglrxinfo
  1. OPTIONAL - you can try this for fun, in terminal type:
fgl_glxgears

Original source: http://www.youtube.com/watch?v=52JRCddtZLk