Summarize:

If you're facing the front of the Xbox, the hard drive should be on the right and the DVD drive should be on the left. The hard drive is most likely shiny, and the DVD drive is most likely dull gray with a yellow sticker on it. Grip the connector firmly on each side and pull it straight back from the hard drive. The cable might be snug and difficult to remove. Rock it back and forth if you are having difficulty pulling it straight out. You can find this screw on the divider between the hard drive and the DVD drive. Once you remove the Torx 10 screw holding it in, you can pull the tray holding the hard drive directly out of the case.  The hard drive is attached with a power cable. You most likely won’t need to remove the power cable to remove the hard drive from the case, but if you are swapping out the hard drive you can pull the cable directly out from the hard drive. You can remove the hard drive from the tray by unscrewing the small screws that hold it in. Remove the cable the same way that the hard drive’s cable was removed. Pull it directly out from the DVD drive. There are two screws holding the DVD drive in, one on each side of the DVD drive. Once the IDE cable and screws have been removed, you can pull the drive straight up and out of the case. Pull it directly out of the drive. Be careful when removing the power cable as it is Xbox-specific and can be difficult to replace.
Locate the hard drive and DVD drive. Unfasten the IDE cable (broad gray cable) from the back of the hard drive. Remove the screw from underneath the IDE cable with a Torx 10 screwdriver. Lift the hard drive tray out of the case. Detach the IDE cable from the DVD drive. Remove the screws from the DVD drive. Pull the DVD drive out. Remove the DVD power cable.