I have a fairly heavily upgraded (see my system specs) Dimension E520 and I am running a BFG GeForce 8800GT OC in there without any issues.
As others have mentioned, you will need to make sure that the internal onboard graphics are disabled and the 8800GT is enabled in the system BIOS. Press F2 at the Dell logo when you switch on your PC and go from there. I can post exact steps when I get home tonight if you want me to.
I did install a more powerful power supply (450W) not only because I wanted to make sure the new graphics card got enough power, but because I needed a PCIe power connector for the 8800GTOC.
The standard power supply in a Dell Dimension E520 doesn't come with a PCIe power connector. At least mine didn't. That's one thing you will need to check. If your 8800GT card has one, you'll need a power supply which has a plug to supply it.
Here's a PCIe power socket on a Radeon Card for example:
Before I upgraded my power supply, I used the 8800GT OC with the stock power supply and connected the PCIe power using an adapter like this:
...the power supply did run very hot, so I upgraded it.
I hope some of this has helped you!
Let me know if you need step by step instructions for changing your graphics card settings in the BIOS, and good luck!