Replace the glass of the window you plan to put your arm through with your specially cut glass. Your glass should be taller than the window frame, and the bottom should have a hole cut out where you can slide your arm through. It would also be a good idea to attach two handles to the glass, for your assistants to hold, and to have a frame in which the pane of glass can slide.
Have two assistants stand outside, where the spectators are, and hold the square of paper against the bottom of the glass.
Go inside, and have your other two assistants slowly raise the pane of glass up, so that the hole in the glass rises above the bottom of the window frame.
Insert your hand slowly through the hole, and through the paper on the other side. The paper is to conceal how you do the trick.
Retract your hand and have your assistants lower the glass again.
Go around to the other side of the glass and have your assistants remove the paper, to reveal the solid pane of glass below.