Here is what I have learned about hatmaking so far.
1) Obtain or order at least one hat body. This is the unblocked, crudely shaped proto-hat.
Hat bodies come in two basic shapes. One is the hood, shown in the first picture above. It is roughly conical, and optimal for hats ranging from brimless to a moderate brim. The second is the capeline, which has already been shaped to include a broad, flat brim, and is the optimal starting point for a broad-brimmd hat. I've been able to make a broad-brimmed hat from a hood, but it's more work, and you can get a broader brim starting with a capeline.
You also have two basic choices for material, wool felt or fur felt, usually rabbit fur. The top photo shows a fur felt hood in the center flanked by two wool felt hoods. Fur felt is stiffer, crisper and less floppy, and costs at least twice as much as wool felt. In the 21st century, fur felt is the norm for a fedora of good quality. High quality medieval hats, like that of Chaucer's merchant, were made of beaver fur felt. The greater stiffness of fur felt is particularly desirable for broad brimmed hats.
You can also buy long hair fur felt bodies. The hair is visible and palpable on one side instead of being processed into a smooth surface. This can be a pleasant effect on the inside and upturned brim of a hat, although this kind of felt seems a bit less stiff than regular fur felt.
If you're going to the trouble of making or buying a hat block it seems sensible to order several hat bodies. Leko has a good assortment of bodies and other millinery supplies.
2) Make or obtain a hat block. Wood is traditional. I carve mine from Owens Corning pink polystyrene insulating foam with a bread knife and finish with a sander and a sanding block. I made my first block with expanding foam filling a masking tape skin. It's softer than the pink foam and doesn't sand as smoothly, and I no longer use that kind of foam for new blocks. Remember to clean your block after sanding before you block with it.
Hat Shapers sell inexpensive ABS plastic hat blocks. I don't know how well they work, and they don't have all the shapes you'd want for medieval hats, but some look applicable. If you try them, let me know how they work for you.
Having separate crown and brim block pieces increases your flexibility. I can also remove the top piece of my Robin Hood crown to make a flat-topped version.
3) With my current blocks, I finding wrapping the crown or, in the case of the Robin Hood hat, the entire block with cling wrap makes it easier to force the body over the block and remove it later.
You will want an elastic hairband big enough to pull over the circumference of the bottom of the crown. If you are making a hat with an upturned brim a salad spoon like the one shown in the second photo is useful for working between the crown and the brim: a long handled shoehorn will also serve.
With everything gathered, I fill my bathroom sink with the hottest water I can get from the tap, putting the body under the tap like a bucket. When the crown is full I tip it over and submerge it, weighing it down with a full water glass. I let the body soak for severable minutes until it is pliable and easily stretched.
Let me start with a Robin Hood hat.
I pull the body from the water, letting some of the water drain off. I make a first guess at turning the brim up and force the body over the block, pulling and pushing it downwards until it conforms to the block, and moving the turn of the brim upwards or down as needed. Use the salad spoon as needed to pull the crown downwards behind the brim. Slide the elastic hairband down to bottom of the crown.
Now grasp the front of the brim with one hand while you brace the heel of your other hand against the front of the crown just above the bill. Pull the brim forward and down until it conforms with the bill of the block.
At this point the upturned part of the brim may not be turned upwards as steeply as you want. You can pin the bottom of the brim against your work surface with the salad spoon while pulling the upper edge upwards, stretching the felt. Start at the center rear and work gradually to the front on both sides. This may create some puckering at the top edge of the brim: smooth that out.
Update: If the upturned brim needs additional shaping, I now find it easier to mold the brim over an extended brim block before turning it up, as shown in the last photo. You may want to compress the brim over the bottom of the block with another elastic hairband.
Try to work quickly: the body will soon become harder to work. You can re-soak the body if you need to do more blocking.
Let the hat dry before trimming away excess felt. I let the hat dry on the block until it can hold its shape and then stand it on a glass or round Tupperware container as a stand to complete drying.
The second photo shows the block for a Robin Hood hat and blocked hats before and after trimming away excess brim.
If you start with a capeline a broad brimmed hat should be simpler. Pull the body down over the crown and stretch the elastic hairband over the bottom of the crown. You may need to temporarily turn the brim up to get clearance to complete pulling the crown onto the block. Then pull and stretch the brim down onto the block brim. The third photo shows the block and the narrower brimmed hat produced from a hood body in the center, with a hat made from a capeline at far left.
The 4th photo shows three hats made from low crowned block without a brim block, and the block.
At far left the body was pulled onto the crown and the brim turned up, and an elastic hairband pushed down to the bottom of the crown. I placed a belt weight leather spacer between crown and brim at the top of where I expected to trim the brim, and an elastic hairband over crown, spacer and brim at that point. I tugged the brim upwards from above that point until I created a narrow vertical brim without puckers. The excess was then trimmed away. This simple cap was worn by peddlers, laborers, small tradesmen, cooks and bakers by day, and by gentry as a nightcap.
To its right is a simple brimless cap, often worn by clergy and scholars, and sometimes by other laymen.
The third used the low crown block without a separate brim block and a single layer of wool felt. In blocking, wet felt was pulled forward from the crown block to create a bill in front of the crown. I stretched an elastic hairband around the crown just above this bill to keep the hat body from being pulled away from the upper crown.
You can use two hat bodies in contrasting colors on the same block to recreate what is often seen in medieval art: a hat with a contrasting upturned brim or lining. Two cautions:
Not all commercial hat bodies are colorfast. If you want to make a hat using two layers in contrasting colors, it is well to know if either color will run in hot water.
Also, not all felts play well together. I recently tried to use a fur felt outer layer and a wool felt inner layer. They did not cooperate.
In contrast, two layers of wool felt were willing to become a single hat.
If the hat is too floppy stiffness can be added or restored with hat stiffener. One hatmaker warns that the felt should be absolutely dry before stiffener is applied, or white marks can appear on the surface. This agrees with my experience from before I read her advice.