Step 1: Prepare the scene/set dressing
The first step is to place some objects around your display screen so they are partly obscured by it. This will help to sell the illusion.
The next thing you have to do is choose where in your room you want the monitor to appear transparent from. In other words, which one vantage point in space do you want the illusion to hold up? Do you want it to be right in front of the computer, so anyone using it gets to enjoy your hard work? Do you want it to be at eye-level if someone peeks over the cubicle partition to see what you are working on? Do you want it to be from the eye level of your 6 year-old so if he stands in the doorway he "gets it?"
For this instructable, I chose a nice "standard working distance" away from my computer so I could enjoy the view myself.
When you know which vantage point you are going to target, "dress the set" with the items you have gathered to sell your illusion.