first, I would determine the location of the intended window. Then draw the square onto the door. Then at each corner, I would drill a hole through the door and through the outer skin. This will be the pilot holes for the jig saw blade. The hole should be as wide as the longest blade in the jig saw.
With the hole cut out; here is where you carpentry skills will come in. I would guess that the thickness of that door would be about 1 1/2 inch. I would then get some 1 x 4's and rip them down to that width. dry fit them in the square to make a inner square with butt intersections. Have the top and bottom boards the longest and the sides would be sandwiched in between the top and bottom rails.
Now take the loose boards out and now lay them out on the table and fasten them together as they were dry fitted in the door square hole. Now, get a pane of glass the size of the inner square. Now, have some small 1/4 round molding on site.
Here comes the tough part. Place the pane of glass in the center of the square frame. Determine the center on all four sides and pencil in the area where that pane will sit on all four sides. Remove the pane and now, with a mitre saw, and the 1/4 round, you will build a framing mitered square with the quarter round on both sides of the glass to actually hole the pane in place and to dress it out. Once done, you now have the frame, with the pane, and the mitred quarter round in place. So, you have one piece.
Now slide the frame into the hole as it was when dry fitted. You may need to knudge this in place and maybe even shim it in several places. Do not worry at this point about the rough cut of the door not being neat, we will picture frame both sides of the door with molding that will affix the frame in place and attach it to the door.
Now, find that nice molding that will attach to the inner framing square and overlap over the actual door and cover the rough door hole that you cut.
Mitre the corners on both sides of the door. now, with finish nails nail the molding to the frame and with a drill, drill a pilot hole through the molding and into the door. Counter sink the opening of the hole in the mitred frame. You should have a hole in each side of the frame and on both sides of the door. eight in total.
Now with a drywall screw, screw the fastener in the hole and into the door, with the head counter sunk, you can spackle the screw hole and it will not be seen. Caulk it in good and prime it and paint it. This should be that.