I wanted this block to have more of a pieced look, so I devised the following method. Many people simply applique the shapes onto the background and that's just fine.
Here's what I did.
Cut two 6" squares out of your main fabric.
Print or trace the block diagram onto the dull side of freezer paper and cut out as follows.
Be careful to keep the center shape as intact as possible.
Iron the center shape onto the center of one of your fabric squares using a hot, dry iron.
Iron the "melons" onto background fabric and cut out, leaving an 1/8" seam allowance on one side and a bigger one (I left about an inch) on the other side.
Position one of the melons on the square, carefully lining up the edge of the freezer paper melon with the edge of the inside shape. Use a light table or a window to get the alignment correct. Baste.
Applique the melon onto the background square along one side, using both the freezer paper melon and freezer paper inside shape as guides.
Repeat this to applique all four melons onto the background square.
Using a hot dry iron, iron the freezer paper square you have left onto the center of the other main fabric square.
Cut out the center, leaving an 1/8" seam allowance all around. Clip into the seam allowance at 1/4" intervals up to about 3 threads from the edge of the freezer paper.
Carefully center this square on top of the previous square (with the melons), and baste together. Using the reverse applique method described in previous blocks, applique the top square to the bottom square so that the melons are peeping through the circle.
Print or trace the diamond shapes from the diagram onto the dull side of freezer paper. Iron to the right side of background fabric and, using the needle turn applique method described in previous blocks, and the diagram as a guide, applique the diamonds to the four corners of the block.
Trim the block to 5" square, being careful to center the circle in the block.