there are several ways to make these blocks.
the easiest is to cut circles from one fabric, center and permanently fuse them to the background and stitch around. you will "lose" the circle of background fabric underneath.
another way is to use a temporary or easily removed fuser (like super lightweight Stitch Witcher). after the top circle is stitched, you can flip it over and very carefully cut out the back circle. the trick is to separate the fuser from the top fabric. you can do that by carefully inserting a straight pin between the layers and wiggling it to get them apart. unless you are trying to save as much fabric as possible, i don't recommend this method. it's pretty risky unless you have a steady hand and scissors with a small and very sharp tip.
a third way is to cut circles out of the center of the background fabric that are 1/2" smaller in diameter than the top circles. center the top circle over the empty space. either use a lot of pins or teeny tiny drops of glue to "nail" down the top circle. (if you're worried about the glue making the circles stiff, use a school glue - like Elmer's. it'll wash out later.
if you plan to turn the edge of the top circle under before stitching it down, and want to cut out the circle from the background fabric, make sure to cut out circles that are at least 1 whole inch smaller than the top circle. (the wider the "seam allowance" you turn under on the top circle, the smaller the background circles need to be.)
of course, you could really drive yourself crazy by cutting the background circle 1/2" smaller that the top circle and then stitching them together all the way around. send away all children under the age of 18 first, though. if you don't cuss like a sailor now, you will by the time you've assembled your first one. :lol: