For my Halloween costume this year, I needed to give the illusion that I was outdoors, so for my background I made a moon and stars foam core backdrop.
Step 1: Preparing/Painting the Backdrop
First, I found a piece of foam core that fit the width/height I needed for my costume. Then, using a battery powered closet "pop light" as the full moon, I figured out where the "moon" needed to be on the costume and drew out the circumference in pencil. I cut out this circle carefully using a blade, starting with cutting it a bit smaller than the actual pop light (always a good idea to start with a smaller cutout and cut a bit more as you go, rather than cutting out a larger than needed hole!), so the light fit through the hole snuggly to hold in place. I then removed the light and painted the backdrop with dark blue/shimmery white (for the clouds/moon glow). Since I knew where the moon would be on the backdrop, I painted a circular whitish "glow" around that cutout.
Step 2: The Moon
After that was dry, I pushed the pop light into the pre-cut hole and secured the circumference with a bit of hot glue from the back. I opted to add a moon patterned/textured cover onto the pop light, but I don't think it was necessary. If you want to do the same, I achieved this by taking a piece of clear laminate paper, cut in a matching circle size as the pop light, and painted lightly with a white/gray glow, using my fingers to create circular craters (your different finger sizes created different craters!). I secured this to the pop light with 2 sided adhesive dots.
Step 3: The Stars
Finally, I used battery powered "rice lights" for stars, and poked holes through the foam core where I wanted "stars." I then went in from the back and secured each rice light with a dot of hot glue. Keep in mind during this step where you are planning on affixing/hiding the battery pack of the rice lights, so that you move in the right direction and end with the battery pack near its intended hiding place!