Pretty much every modern game I’ve played included a DirectX update in the install routine, but just in case you run into one that doesn’t automatically update, or doesn’t do it properly, you can always download the latest version from Microsoft’s DirectX website. It is recommended that you do it this way because you are downloading the entire install package and it’ll have all the resources it needs to properly update your system.
After you have installed or updated your version of DirectX, be sure to test your computer to make sure everything is working properly. Follow the steps above to run ‘dxdiag’ again, and this time wait for the little meter in the bottom left corner of the DirectX Diagnostic Tool window to finish loading. After that, click the Next Page button and go through each section – Display, Sound, etc – and make sure there are no errors reported. In DirectX 10 and 11, it runs the tests for you, but in older versions you may actually have a Test button under each section.
If your games still don't perform that well after a DirectX update, it may be time for you to get a new video card.