Cut out the pieces along the compass marks.

Spray the pieces with water until they are really wet. The blue lines will disappear. Press with a hot iron until dry. It may take a couple of rounds of wetting and ironing to completely erase the blue marker, so repeat as necessary.

The covers for these cuff links are basically just tiny yo-yos. (Heather Bailey has a great yo-yo tutorial on her website if you don't have any idea what I'm talking about.)

Thread a needle with your white thread and tie a knot at the end. Using a small running stitch sew a 1/16-inch hem all around the circle. The hem should fold onto the wrong side of the circle.

Go all the way around the circle as shown above. DO NOT CUT THE THREAD! Keep the thread on the needle.

Cut a piece of the batting in the same size as the head of the cuff link. 

Place this little batting bit in the center of the muslin piece on the wrong side.

Place a cuff link  firmly on the batting.

Pull the thread to cinch the fabric around the stem of the cuff link.

Once its in place, pull it very tight and tie a little knot on one of the pleats as near to the center as possible.

Wrap the thread around the base of the cuff link several times tightly and then tie another knot.

Hide the thread end inside the gathers and clip it. The back should look like this.

Repeat for the second cuff link and you'll be done!