The real key to not breaking anything when you’re taking apart your Xbox 360 is that when it’s done right, everything will just pop open, do not ever pry or you’re going to be a very unhappy camper.
I’ve put together a video here to show you exactly what to do and how, what not to do, and in what order you should do them in–follow the steps in the exact order that I do them, don’t be afraid to just pause the video whenever you need an extra moment to do something properly. It will take a lot longer than the length of the video to do this, no worries just be patient and you’ll guarantee that you won’t damage your xbox.
If you’re doing this to repair your Xbox due to the Red Ring of Death (RROD), the best guide to doing this properly, hands down, is The 3 Red Light Xbox 360 Repair Guide, I highly recommend you get that and follow it so you know what you’re doing. Have a look:
Additional Resources and Further Reading
Here’s a really great site that goes into detail for each step in a step-by-step set of instructions with pictures for each point of the disassembly.
This is a comprehensive site for do-it-yourself Xbox 360 repair, these guys are awesome, there’s nothing you can’t fix on your own if you’ll just refer to their site.