This tutorial gives step-by-step instructions on how to update your video drivers.
Dawn of War and Company of Heroes support cards with either the ATI or the Nvidia chipset. ATI cards have the word "Radeon" in their name, such as "Radeon 9800 Pro" or "Radeon X800", while Nvidia cards are called "GeForce", for example "GeForce 8800GS".
If you're not sure which card you have, refer to the How do I find out which video card I have section.
The next two posts will tell you how to update your drivers depending on your type of card.