fold the round item you want to border- in half- then in half the other way- so you have a 1/4 piece of pie-
trace the edge onto freezer paper- add seam allowance to the side next to the fabric piece- measure out the width of the desired border- draw this line- again- add seam allowance- add seam allowance to each short end. (for joining the four pieces together) cut out on the outer lines.- fold your border fabric to either 2 or 4 thickness'es- press your freezer paper template to the fabric- cut out- join the short ends into a circle- fold (crease) your border circle into 4 new sections ( between the joined sections) so you have 8 match points...then fold your large circle again so you have 8 match points. place the border circle ontop of the circle- match your (match points) & pin- the distribute the areas between the pins & pin every couple inches- stitch into place- carefully clip around the circle to the stitching line- (being careful to not cut your stitches) then press toward the border fabric.
Ricky Timms has a pretty good tutorial for Circular sewing- check out his website.