Fletching (from where the Fletcher gets his name) is the feathers that are fixed to the arrow shaft and makes the arrow spin. Traditionally these feathers came from a goose, but thanks to the Victorians shift in tastes the goose lost it's place on Western dinner tables and was replaced with the North American Turkey. Hence nearly all commercially available feathers are dyed Turkey feathers. Undyed Turkey feathers are brown and white and are an acronym in the quivers of the occasional Robin Hood.
There are normally three feathers per arrow and are arranged so that one feather is perpendicular to the bow when nocked on the string. To aid the archer in nocking the arrow this feather was usually a different colour than the other two and so came from the cock bird - hence the name for this feather is the cock feather (although also sometimes referred to as the "index" feather by people who are embarrased by the word "cock").
So traditionally they could be made from goose feather (grey or white) but also peacock feather was used if a person had the coin. As now, feathers could be dyed also. You can therefore choose two colours to make your arrow different from all the other arrows on the field, but there's nothing stopping you from having all the feathers of the same colour.
Some folks may want arrows for speed shooting or SCA Comabat Blunts which requires on two or four feathers per arrow shaft (thus making the way the arrow is nocked unimportant). If you're that person now's the time to ...
Write down if you want a normal 3 fletched arrow or a two or four fletched arrow. e.g. normal 3 fletched arrow
Write down the colours of you fletching and/or the colour of the cock feather if you want to use a two colour scheme per arrow e.g. two blue, cock feather red
Now the harder part, what size of fletch and how do you want them cut? Although known by different names medieval fletching were cut "Hunting Style", "Triangular" (with the back cut straight "Triangular 90 degrees", with a bit of an angle "Triangular 110 degrees", "Triangular Natural Line"), "Curved" and "Hog's Back" or "Sadle-back". Triangular cut is the most economical to produce and it's this cut that appears to be used for medieval war arrows. Curved could have been used for war, but was more likely used for hunting and Hog's Back apparently is the best cut for long distance shooting.
Modern fletchings come in two popular types - "parabolic" (which is similar to Hog's Back and the longer versions which are similar to Saddle-Back) and "Shield Cut" which is similar to Hunting-Style. Shield Cut is basically a triangular cut with the end removed so that the archer's fingers don't crush the feathers. For simplicity the size of the fletching affects two things (1) Stability and (2) Speed. A small fletch will be quicker but less stable, a large fletch will be slower but more stable. Modern fletchings can be as small as 2" long and can, if found, go up to 5.5" long. For a medieval looking arrow you'll need at least 4"+ long fletches as medieval arrows had heavier arrow heads and so required the more stable, longer fletchings. Longer fletchings look better for the traditional archer too.
I can modify a pre-cut store bought fletch to make a medieval version e.g. take a 5" Shield Cut fletch and make a 4.5" Triangular cut fletch by removing the back 0.5". Anything longer that 5" will usually involve purchasing a whole feather and cutting it as need be. A feather can cost twice as much as a pre-cut fletch.
Pen and paper time. Write down...
The length of the fletch. e.g. 5 inches
The style cut of the fletch. e.g. triangular 90 degrees
If you're not sure put question marks here and I'll suggest something based on your persona and persona's use for the arrows you gave me in Step 1.
Now move onto Step 5 - Binding