Best place to start along with the reading suggested already is to register with www.eurasia.nu you can then download loads of the tools and guides.
These would be a place to start.
1:
FTP Guide PC To Xbox Manually/Auto
2:
C-Xbox Tool 2.0.5
In simple terms, its a s easy as this.
Configure Xbox with IP address, and connect to via an FTP server on your PC.
To do this, both devices have to be on the same ethernet network, via Hub, Switch or cross-over ethernet cable.
Start FTP server on PC and connect to the Xbox.
Naviagte to the DVD drive directory, and select the disk contents and transfer to the PC, store in a folder on the PC.
Run C-Xbox tool and create ISO ready to durn to DVD.
Burn the DVD using Decrypter or similar program.
Stick it in the Xbox and play.
The Xbox needs to be either soft-modded or chipped to play the backed up game.
Chipping can be done yourself (not good idea) or by a company (Google one in your location).
Softmodding is possibl, but you need the guide, a certain game (there are a few you can use) and a memory card.
Personally I went for the chip, its easy and does everything, you also get a larger HDD done, although I did mine myself, you can then back games up to that instead of/aswell as DVDs.
