While this is written with my Raspberry Pi in mind, this 'Ible can, of course, be accomplished with any device that you have the desire to hide. Whether it be an Intel Edison, an Arduino, or any other single board computer, all it takes is a little imagination and some digging to find just what you want.
Step 1: Step 1: Gather and Prepare the Parts
As you can see, I have a decent amount to hide along with my Pi. There's the Pi, itself; the Pi's power supply; a powered USB hub with power supply; and a pair of external hard drives with connecting cables.
I was helping to clean someone's house a few weeks ago (they were moving up north) and I came across a plain, cheap DVD player. With no knowledge (or care) of its working status, I decided that this would be my hidey hole. I finally got around to gutting the device (that's a different 'Ible altogether), I set aside the various motors, the laser diode, connectors, and anything else that I figured I might need in the future.
Once all of the unneeded parts have been removed from the case, break off the three upright posts on your right (they held up part of the guts and will only get in the way) as cleanly as possible and move to step 2.
Step 2: Step 2: Cram It All in There
Now it's time to get imaginative. Take everything that you'd like to be inside of your case and begin playing Tetris with it all. Once you have a modicum of order about your equipment, begin considering the wiring of all of your pieces. Ideally, one would be able to find cables that are on the shorter end of short so that you don't need to bunch up the cables as you can see that I've done.
My recommendation, depending on the amount of equipment that you are placing within your case, is to use velcro pads between the case and the piece to cease movement of the parts if the case is moved, but to facilitate removal of the parts should the need arise for repair.
Step 3: Step 3: Button It Up
Assuming that you haven't thrown all of your stuff across the room or given up and gone out for drinks, you're done. Close up the case, put it in the obvious hiding spot, and enjoy your cloud/media/web server/streamer/desktop.