Begin with a base - whatever shape you want - rectangle or oval works best. I made a round penny rug a few years ago and really it is only useful on a round table. I also cut a piece of thin quilt batting to add stability and a little thickness to the piece.
Then add the outer pennies -- these can be round or U-shaped. Try using a bright color on a dark base for contrast.
Then begin adding the details on the middle. Start with a branch cut from a brown patterned wool piece this doesn't need to be very wide or long as you can piece it together. Add some leaves and a flower or two or three. Cut out a bird or two and fit this onto the branch. Don't sew all these shapes down until you have shifted things around and are satisfied with the look. Add or subtract pieces as needed to fill the length of base. The rug I made is not very big so I only put one bird in it as the central figure. Then use your embroidery floss to sew everything onto the base and add some decorative stitching for interest.
At this stage I tack the penny edge with some contrasting thread because when I add the backing I am going to stitch around the entire piece which will include the edge. I then add a back to cover all my stitches, remove the thread and finish the whole thing off with a good pressing with an iron and a wet pressing cloth.
Don't worry that your stitches and shapes are not perfect! This is an art form that is "primitive" in its interpretation -- sort of a Grandma Moses, folk art piece. Sometimes when things are too pristine we become afraid to use them. So - go ahead! Try it.