As with anything there are several ways of doing the same thing.
I would start with the easy...cut a circle of fabric that includes the seam allowance, cut the same size circle of fusible interfacing (the lightweight kind, with dots of glue on one side) sew the two circles together (right side of fabric against dots of glue). Cut a small slit in the interfacing and turn right side out. Use a chopstick or other such tool to smooth out the edges. The dots of glue should be on the backside of the circle fabric (dots facing out). Place on background fabric fuse into place and sew around by hand or by machine.

You could also use freezer paper templates-cut the size of the circle you want, iron to backside of circle fabric cut out. Remember to include seam allowance. Use your sewing machince to stitch a basting stitch in the seam allowance and then pull the ends of the thread to gather the seam around the paper. Starch the edges then iron dry. Remove basting stitches and paper (paper can be use several times).
Place on background sew by hand or machine.

Please don't be afraid of circles, one of the easiest shapes to applique. :thumbup:

I make my circles this way as well, the thinner the back fabric, the easier it seems to be.

I use "Perfect Shape" no melt plastic from The Stencil Co
I cut a circle from the plastic then use it as a template for cutting the fabric about 1/4" larger. then with iron turn the edges over and iron. I might spray starch the edge and then iron. Perfect every time.

I have made reversable quilts with this method


* I had problems making circles too, before I learned this method. The circle would look great, until I stitched it, no matter how careful I was. I made almost all of my circles this way now..*

I do as Holice does...with excellent results. I love circles. :oops:

Use the method bluteddi gave, but use iron on fusible. Then when it's all turned, just press it on your piece.

is anyone notching in the SA?

on the muslim turn birth one, or pressing template one, or needle draw one?

Mark around the circle on the fabric and then glue baste the circle edges right on the drawn mark leaving just a little of the marked line showing. Stitch on the marked line. Lots of heavy starch to hold the circle shape firm is a great help.

I find it helps to have the underside fabric just slightly smaller, maybe 1l8 inch. Then when you press, the right side fabric rolls over the wrong side fabric so it doesn't show. Also, you can use the light weight interfacing to reduce bulk. And sometimes I'll trim the edges with pinking sheers rather than notching.

That's exactly how I do it and get perfect circles every time.
It will work with a yo-yo template too... Your correct about not using anything that the iron will melt..