I love doing dimensional quilts with shadows and make them often. If you want a drop shadow (the kind that makes it look like something flat is floating above a surface), the easiest way to do it is to cut your shadow fabric using the same template used for the circle that is casting the shadow.
Once that's done, there are two ways you can proceed. You can appliqué the shadow directly to the background before adding the circle or you can appliqué the circle to the shadow and add them to the background as one piece.
Either way, decide how much of the shadow you want visible (a bigger shadow will mean the circle is floating higher off the surface) and mark a faint line along that arc. Cover that line just slightly with the circle. Treat the edge of your shadow the same way you treat the edge of your circle (turned, raw edge, etc). You can back your circle with light fabric to prevent the shadow fabric from showing through, and I would suggest you trim the shadow so not too much of it is underneath the circle.
Some "don't forgets" for shadowing:
Always remember the direction of the light. Keep it constant or you'll confuse the viewer and lose the shadow effect you're aiming for.
Remember that the shadow color is always a duller, darker color of the background. It has absolutely no relationship to the color of the object casting the shadow at all.