I read of the tutorial and history on making your own Dorset Singleton buttons over at Craft /Stylish (the concept dates back to the 1600 and named Singleton after the family that first began making them and Dorset as tthey originated in Dorset, England.)
I made the button using the plastic ring off of a plastic soda bottle (it is the ring that the lid twists off of) as my base.
To make a template of for the fabric to cover the plastic ring, I used a soda can and drew around the perimeter with a pen, then cut out the circle.
Here is a comparison of the template size to the plastic ring.
Pin the template to the fabric then cut to make a fabric circle. Hand baste approximately 1/4 inch away from the edge of the fabric all the way around, then put the plastic ring in the center the pulled the thread (like you do when you are making a fabric yo-yo).
Pull the fabric taut then hand stitch to secure the fabric.
Turn the button over and hand stitch close to the edge of the plastic all the way around the perimter to produce the above button.