Do not use the Mesa drivers. They suck.
For ease of use, use the Synaptic Packet manager to install the following.
Search for fglrx
Select fglrx-amdcccle
Select xorg-driver-fglrx
Click Apply
Open Administration > Hardware Drivers.
Activate the ATi/AMD proprietary FGLRX graphics driver.
Best Radeon drivers you can get for Ubuntu and they're straight from ATi/AMD.
The rEVOLution is not being televised