Step 1: Lay it out
lay down two perpendicular lines in a cross. Now place your square against two lines and hold or clamp in place.
For the trammel bar I bent up the end of a strip of cardboard and taped on a fine point sharpie. then I punched holes and inserted sharp pencils for the points
For the points you need to measure from the marker point to the pencil hole 1/2 the major axis and again for the other hole 1/2 the minor axis. In this case I wanted to overall to be 12" x14". so the pin holes were 6" and 7" from the marker tip. that's pretty close together to and makes it a bit tricky to operate, but You can do it.
now poke your pencils or whatever you are using for points through the holes and run them along the legs of the square. start with one point at the corner and draw it down the vertical leg while the other is run across the horizontal leg of the square. If bothpoints are kept tight to the square, the marker will have traced out one quarter of an elipse.
Now just flip the square to each remaining quadrant and lay out that section of the oval.