In the following steps, you will be releasing the six clips highlighted in red.
Each clip can be undone by inserting a metal spudger underneath the bottom edge of the clip. Once underneath the bottom edge, simply prying away from the console will free the clip.
Orient the console so that the left case is facing toward you and the faceplate is facing toward the right.
Insert a metal spudger through the front-most slit on the left edge of the top bezel and between the bottom edge of the clip and the left case, as described above.
Simultaneously rotate the spudger away from the console and pull up on the top bezel to free the clip.
You will hear a "pop" signifying that the clip cleared its catch.
In the following steps, you will remove the bottom bezel, which is attached to the rest of the console by the six clips shown.
The clips shown in red can be detached by inserting a metal spudger underneath the bottom edge of the clip. Once underneath the bottom edge, simply prying away from the console will free the clip.
Turn the console around so that the faceplate is facing to the right and the right case is facing toward you.
Insert the spudger into the rear-most slit on the right edge of the bottom bezel, and wedge it behind the clip by pushing the spudger down while pushing the tip of the spudger against the right case.
Simultaneously release the clip and pull the bottom bezel up.
This clip is especially hard to remove. Some force will be required to insert the spudger correctly.
Opening your Xbox 360 any further will require breaking or removing the warranty sticker on the outer case. Your Microsoft warranty for any components not directly attached to the logic board will likely be voided by removing this seal.
Thank you to who ever posted this! The directions are clear, you just have to read than reread, go slowly and don't force anything and most importantly do not get frustrated. My grandpa always said "if it is worth doing, do it right the first time.", and "measure twice, cut once."
Care is required from Step 5. Do not slide the spludger down the back of the faceplate. This may (it did) damage the ribbon to the power and eject button on the front plate. OOPS.