First I want to clarify that I did not write this guide I am merely rewriting and publishing.
Marian Lux wrote the original at askubuntu.com. All credit goes to him.
Link to original post: here.

This tutorial worked for me personally, and I have AMD Radeon HD 4600M integrated graphics card in my laptop.

Pre-Install:

Three terminal-commands:

Code:
sudo apt-get install build-essential cdbs fakeroot dh-make debhelper debconf libstdc++6
sudo apt-get install dkms libqtgui4 wget execstack libelfg0 dh-modaliases
sudo apt-get install linux-headers-generic xserver-xorg-core libgcc1
Optional if 64 Bit - two terminal-commands:

Code:
sudo apt-get install ia32-libs lib32gcc1 libc6-i386
cd /usr ; sudo ln -svT lib /usr/lib64
Download from this direct-link: https://launchpad.net/~andrikos/+arc...-archive-extra the files and this two .deb packages into an empty folder

xserver-xorg-video-intel-dbg_2.20.0-0~andrik1_XXX.deb
xserver-xorg-video-intel_2.20.0-0~andrik1_XXX.deb
where XXX should be your architecture identifier (x86 or amd64)

Execute the following two terminal-commands in the folder with downloaded .deb files:

Code:
sudo dpkg -i xserver-xorg-video-intel*.deb
sudo dpkg-reconfigure Xorg
Then reboot your machine

Note - this is from the PPA: https://launchpad.net/~andrikos/+arc...filter=quantal

Important - There have been released a security update for "xserver-org" from the official Ubuntu repositories which mad the system crash again (no login screen). All you have to do is to install the newest two xserver-org-video-intel*.deb's (downloaded and installed as described above) from the PPA https://launchpad.net/~andrikos/+arc...filter=quantal again. You can also add this PPA on your system for preventing this issue. The PPA may have too many other packages, so you may want to do it (downloading the two .deb-files and installing them) manually. Another solution is, to de-select the "xserver-org"-packages if there are official Ubuntu security updates available.

Installation:

Get the current ATI Catalyst driver e,g 12.11 Beta (Marian Lux have tested it with this release):

Code:
wget -c http://goo.gl/QRHCk -O catalyst-12.11-beta-x86.x86_64.zip
Unzip the .zip and make it executable. Then go to the folder with the unzipped .run-file in terminal and type:

Code:
sudo sh ./amd-driver-installer-XXX.run --buildpkg Ubuntu/quantal
Replace XXX with the correct name of the file

Install the created .deb-files with the following terminal-command in the current directory:

Code:
sudo dpkg -i fglrx*.deb
Post-Install:

Enter the terminal command

Code:
sudo aticonfig --initial -f
Reboot your system

Code:
sudo reboot
optional - fixing the bug for direct rendering on the integrated card:

Code:
gksu gedit /etc/X11/Xsession.d/10fglrx
Add the string "/usr/lib/x86_64-linux-gnu/dri/" on your 64Bit system that the line finally looks like this:

LIBGL_DRIVERS_PATH=${LIBGL_DRIVERS_PATH}:/usr/lib32/fglrx/dri:/usr/lib/x86_64-linux-gnu/dri
Add the string "/usr/lib32/dri/" on your 32Bit system, so that the line finally looks like this:

Code:
LIBGL_DRIVERS_PATH=${LIBGL_DRIVERS_PATH}:/usr/lib32/fglrx/dri:/usr/lib32/dri
Links for more knowledge:

http://ubuntuforums.org/showthread.php?t=1930450

http://ubuntuforums.org/showthread.p...930450&page=51

http://www.upubuntu.com/2012/10/inst...ta-driver.html