This is my favorite method for applique (circles or other shapes). I do not have the templates used in this video--Cut them using any template you like. I also use the VERY lightweight fusible pellon instead of the non fusible they use. Make sure you put the pellon so the sticky side will be outside after you turn it right side out. You could cut away most of it if you like, just leave it around the edges. I machine applique around the edges.
I love the hint they give to cut with pinking shears so you don't have to cut slices all around the circle.
http://www.youtube.com/watch?v=M7P0uzhF6uc