Cut out the cracked piece of glass from inside the window with a utility knife. Score the glass along the edges with the knife and carefully hammer out the glass. Scrape off the glass along the frame of the window with a putty knife. Dig the knife into the frame and remove any excess glass from the frame.
Set a piece of plexiglass over the window frame and outline the glass with a black marker so the proper size cut can be made. Set the plexiglass on a flat surface and score it along the cut marks with a utility knife.
Follow carefully along the marks with the utility knife multiple times until the knife goes through the plexiglass. Break the plexiglass into the desired shape and place it into the opening of the window to verify it fits properly.
Slide a tube of window and door silicone sealant into a caulk gun and cut off the tip with a utility knife. Position the caulk gun at the edge of the window along the inside of the frame and run a thin bead of caulk around the entire perimeter of the window.
Set the window into the opening and press it up firmly against the sealant. Run your hands over the entire surface so the adhesive can adhere to the plexiglass. Wipe away any excess adhesive from the surface of the plexiglass with a clean rag.