I used the ellipse (or circle) tool to start.
Or, you could draw a shape on paper and scan it or find a piece of clip art of an egg and make it solid black. We want a plain, unadorned egg to start with.
After reshaping your ellipse into an egg (or scanning an egg, etc.) make it a solid color (black works fine) and save the image. If you don't want to make Easter eggs, draw a circle and make beach balls.
Basic technique in a vector drawing program such as CorelDRAW or Illustrator: Draw the ellipse, convert to curves, use the node editing tools to reshape the ellipse.
Next we move to our paint program where we'll create a mask or a stencil to paint. I'll show you how to paint your eggs (or your beach balls, or any other shape) without worrying about staying inside the lines.