The hard drive in your Xbox 360 is easily removable, but the procedure is slightly different depending on which Xbox 360 you own.
How to remove the hard drive from the original Xbox 360
1. Turn off the Xbox 360 and stand it up right to where the hard drive is positioned on top.
2. Locate the hard drive release button toward the front of the hard drive, and push down.
3. The front of the hard drive should release, so pull up from the front to remove the hard drive.
4. When placing the hard drive back in, place the back side in first, then click down on the front.
How to remove the hard drive from the new Xbox 360 S
1. Lay the Xbox 360 down on its side.
2. Look on the left side and locate the hard drive cover toward the back.
3. Pull the release switch toward the front to remove the hard drive cover.
4. Once the cover is off, pull the tab connected to the hard drive to remove the hard drive.