I like to use baby cording, which I order from http://www.marthapullen.com/. Working with one collar at a time, cut a piece of cording the length of the outer edge of the collar. Fold the fabric at a 45 degree angle (the fold line should be the length of the cording) and cut along the fold line.
Measure in 1" from the cut edge, to cut a bias strip.
Wrong side together, fold the bias strip over the cording. Using a zipper or cording foot, stitch close to the cording to make your piping. I have used a contrasting thread so that it can be seen in the photos. You would normally use thread to match the fabric.
Clip into the fabric, close to the stitching line, at 1/2" intervals.
Check the seam allowance for your pattern and with right sides together, pin the piping to the outer edge of the collar. Stitch close to the cording, over the previous stitching line. * Sew around the curve of the collar in a continuous motion. Stopping and lifting the presser foot to pivot will cause small points in your collar.
Right sides together, pin the collar lining to the collar.
Using the previous stitching line as a guide, stitch the collar and collar lining together. *Stitch slightly to the left of the first stitching line.
Trim the outer edge of the collar, leaving a 1/4" seam allowance. Clip into the seam allowance about every 1/2".