I have a ATI Radeon 3600 and I am kind of new to Ubuntu and Linux. I have read that proprietary ATI drivers aren't good enough and that open source drivers do work very well.
This document explains how to install and use the open-source radeonhd drivers on Ubuntu. This shouldn't be necessary... unless you're having problems with the open-source "ati/radeon" driver that comes pre-installed with Ubuntu.pre-installed with Ubuntu.
EDIT: As JanC pointed out, you shouldn't install the RadeonHD driver if the pre-installed driver works.
I assume you mean "Radeon HD 3600" and not "Radeon 3600".
If you are using a recent Ubuntu version, the proprietary AMD/ATI drivers for that card don't support your card anymore.
Fortunately, the open source
radeon driver is starting to get pretty good now (especially since 10.10, but already good on 10.04 too). And the radeon driver is used by default, so you don't have to enable anything...
I'm in the same boat. I have a laptop with an ATI Radeon HD 3650 video card and I always had to jump through hoops to get things working.
If you are using Maverick however, then things should just work right out of the box for you (i.e. you would by default use the open source driver). If you want to download the proprietary driver then you can go to System -> Administration -> Additional Drivers and download the ATI/AMD proprietrary FGLRX graphics driver.
I did not notice any performance change before/after installing proprietary driver in Maverick so I don't think it's needed. If you using Lucid and below however, I noticed that without the fglrx driver my laptop tended to overheat and automatically shut down, so if you encountered such scenarios and you cannot upgrade to Maverick, try to use AMD's driver.
The radeonhd guide gives great instructions on removing the fglrx drivers, but it is not the right method for lucid/maverick unless you want to install the infrequently updated radeonhd drivers which are different than the radeon drivers.
I would take a look at this page to get a rundown on what the radeon drivers can do : http://www.x.org/wiki/RadeonFeature. It references the drivers as "xf86-video-ati", but they are labled under the "xserver-xorg-video-ati" in the ubuntu repository. You need to make sure that you completely remove the the flgrx files as they can screw up the xf86 install. You will find a lot of good info on the drivers at the x.org website and tips on clean installation.
One thing to note - I am running Kubuntu and ran into problems when I used the non-repository PPAs on the xorg driver. I would try out the ones Ubuntu provides before using the xorg PPAs.