The magnifying glass can be any size, but larger generally equals better. As long as it will fit your shoebox!
I chose a longer box for greater focus flexibility, but I'll explain that later!
Now, on either of the end surfaces, trace around the magnifying glass. This is where it will fit into the box.
I fashioned a small phone/iPod stand from some wire, but use whatever you can! This will go inside the box.
Cut the circle out of the box and insert the magnifying glass. Mine was stuck in there rather crudely, but feel free to make yours look good! I used masking tape to attach the glass to the box.
Finally, you simply put your phone on the stand and put the stand in the box! Move the phone closer or further from the glass to change focus. Experiment! Works best in a dark-dark room.
Here it is with the box lid open so you can see inside. The image at the top is the projection!
Depending on the size and quality of your magnifying glass, your projection may look much better than this. Mine is roughly 12" diagonally, but that can be adjusted by moving it further from the wall.