First check which driver your X server is using; you can see it by running
grep Driver /etc/X11/xorg.conf
given that you are using Xorg and not XFree86 (for the latter one the config file is XFree86Config or something instead of xorg.conf). It might print multiple lines, but it should be obvious which one of them is your graphics card driver.
The driver your X should use in order to get Direct Rendering enabled should be a driver that can "provide" hardware accelaration using your card; usually open source drivers don't do that (well, there's Mesa project if you can't get nothing else). For example ATI cards work with "ati" or "radeon" driver, but those don't provide hardware 3d accelaration; instead the ATI proprietary "fglrx" driver is needed in order to get 3d stuff run at full speed. And since that's proprietary stuff, it is usually not enabled by default on Linux. Some distributions like Ubuntu offer an easy way of enabling this sort of drivers (Restricted Drivers Manager on Ubuntu), in some distributions you just have to hunt down that driver yourself and install it more or less manually, if it even exists. Not all cards have drivers for Linux that provide hardware accelaration; for those cards you can try the Mesa project to get some speed for 3d apps, but if that doesn't work with your card, you're probably out of luck.
EDIT: in addition to installing the driver you of course need to configure your X; alter xorg.conf and replace the driver of your graphics card with the new driver name you installed and make sure any options you might need are enabled. For information on how to configure X, search for existing threads about it here at LQ; they contain lots of useful information.