These are small shoulder capes normally made of white material, in the 15th century they are basic practical shoulder protection; later in 16th century they become fashionable. They are very simple to make: there is a back piece and two front pieces which have a built in collar, it fastens down the front normally with ties and ties under the arms to keep it stable. 

You just need some spare linen and a little linen tape or lucet cording for this garment. The one medieval picture I have seen of a partlet shows with garment in white. I would also suggest that you wear this above your shift and below your kirtle (unless at a Tudor event where they can be worn over the top to hide the kirtles' neck line).
Alternatively you could use some scrap linen to use as a neckerchief  (an oblong piece of material wrapped around your neck and stuffed into your cleavage). 
During the Tudor period, it became popular for richer gowns to be made with a matching partlet.
  1. Take the following measurements - your bust measurement loosely over your kirtle and/or gown, your collar bone to 5cm below your breasts, from shoulder to shoulder.
  2. With these measurements you should be able to make a pattern which looks like this after you have cut out the arm and neck holes. Remember to add a sewing allowance. Fold this pattern  in two and make a copy of this half pattern. The double pattern will be the back while the half  pattern will be used for the front panel.
  3. Cut out your linen and pin the neck pieces together. Take this opportunity to make sure the neck and arm holes are how you would like them.
  4. Sew the neck pieces together with a back stitch and finishing with the overcast stitch.
  5. Fold the rest of the raw edges over twice and sew using the hemming or running stitch.
  6. Add underarm ties and front fasteners.