To get the drivers set up for your AMD card do the following.

System Settings/Software & Updates/Additional Drivers
Select fglrx-updates

If you have multiple GPU’s but only the first is being recognized, you may need to disable the GPU Manager. You will need to edit this file:

sudo nano /etc/default/grub

Change this line to:

#GRUB_CMDLINE_LINUX_DEFAULT="quiet splash"
GRUB_CMDLINE_LINUX_DEFAULT="nogpumanager"

Now update grub and reboot:

sudo update-grub
sudo reboot

To list your GPU’s:

lspci | grep VGA
amdconfig --list-adapters

Now initialize your GPU’s:

sudo amdconfig --initial --adapter=all
sudo reboot

Now run clinfo:

clinfo

You should see your version of opencl:

Device OpenCL C version: OpenCL C 1.2

Now go ahead and set up cgminer, instructions are here:
http://www.reynoldtech.com/mining-decred-on-ubuntu-with-cgminer/

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Notice: The info below is outdated, I’m now using the Ubuntu GUI to grab the additional drivers.

Find the drivers on the official AMD website:
http://support.amd.com/en-us/download/linux

Click on your version of Ubuntu (ex: Ubuntu 14.04 LTS 64-bit)

Download all the fglrx files for your version. There should be 4 of them.

Get to your download directory and copy them somewhere safe like:

mkdir ~/AMD_Driver_packages
cd ~/Downloads
cp *.deb ~/AMD_Driver_packages
cd ~/AMD_Driver_packages

I had to make sure my system had the dependencies

sudo apt-get -f install

Now that you are in the folder you will be doing all your installing from, go ahead and install:

sudo dpkg -i fglrx-core_15.302-0ubuntu1_amd64_ub_14.01.deb
sudo dpkg -i fglrx_15.302-0ubuntu1_amd64_ub_14.01.deb
sudo dpkg -i fglrx-dev_15.302-0ubuntu1_amd64_ub_14.01.deb
sudo dpkg -i fglrx-amdcccle_15.302-0ubuntu1_amd64_ub_14.01.deb

Now reboot

sudo reboot

Check that everything is installed correctly:

sudo dpkg -l fglrx fglrx-core fglrx-amdcccle fglrx-dev

Now run clinfo:

clinfo

You should see your version of opencl:

Device OpenCL C version: OpenCL C 1.2

Now go ahead and set up cgminer, instructions are here:
http://www.reynoldtech.com/mining-decred-on-ubuntu-with-cgminer/