Say you want to draw a hexagon with equal sides. Say you want this hexagon to fit within a circle of a certain size. Go ahead, say it; I’ll wait.
You can do this with just a compass and a straight-edge. First, start off by drawing your circle with your compass. The distance from the pointy end of your compass to the pencil end is the radius of the circle. Don’t change this distance just yet.
Pick a spot on your circle where you want one of the hexagon’s corners to be and mark it. Now stick the pointy end of your compass on this mark and draw a line with your compass that crosses the circle. Move your pointy end to this intersection and repeat, all the way around the circle. The picture below will help if this does not make sense.
Your final mark should overlap with your first mark. You now have six marks evenly spaced around your circle. Connect these marks with your straight-edge, and you have yourself a hexagon.