Step
1 : Draw 2 circles with the same center point. The bigger of the 2 circles has the same radius as half of the Major Axis of the Ellipse you want. This circle is sometimes called the 'Major Auxillary Circle'. The smaller circle has a radius of half the Minor Axis of the Ellipse, and this circle is sometimes called the 'Minor Auxillary Circle'. (green circles) 

Step 2 : Now draw any number of radii for the big circle. Most people use the 60°30° set square as it provides 12 equally spaced radii. However you can have as many radii as you want and at any angle, and all of the angles do not have to be the same. (blue lines) 

Step 3 : Draw lines from where the radii cross the smaller circle in the direction of the Major Axis of the Ellipse. Next draw lines from where the radii cut the large circle in the direction of the Minor Axis, until these lines cut the lines you drew previosly. (red lines) 

Step 4 : And now you are finished. You can draw an Ellipse in any direction with this method, but remember you must know the length of the Major Axis and the Minor Axis, or be able to find them out. 

Remember to draw the construction lines lightly so that the
finished Ellipse stands out. 
