Very few historical outfits are complete without the appropriate headgear. Even when hats or veils aren't particularly called for, the right hairstyle can really put the finishing touch on an ensemble. And since I'm primarily working in the 15th century, I have a delightful variety of outlandish hats to choose from.
The hat I am working on at the moment will accompany the fleur-de-lys gown in the style from the Très Riches Heures. At its core, its really just a padded roll, albeit a very large one and extensively decorated. Because of this, it doesn't call for the wires or stiffening usually associated with hatmaking - just fabric, stuffing, and ordinary sewing tools.
Very narrow padded rolls can be made with just a straight tube of fabric, particularly if it is cut on the bias. As it is bent around the head, the inner portion of the ring automatically forms small folds. However, as they become larger, it becomes necessary to shape the fabric for the roll, as the folding and bunching would become excessive. In making my roll, I still started with a straight rectangle of fabric. I decided that the lengthwise seam would go along the outer edge, and then I put tucks in at even intervals such that the center line of the piece (which becomes the head opening, the smallest point) was much shorter than the two edges. If you're having trouble picturing that, here's how it works in practice: fold the fabric cross-wise at the point you want to put in the tuck. Stitch from edge to edge in a sideways V shape: very close to the fold at each end, and farther away at the center line. Carefully stitch the long edge, leaving an opening so that you don't form a donut which can't be turned rightside out. Stuff, pin or baste the opening closed, and try on. It may require several tests to get it right - expect the tucks to become more severe to shrink the head opening. It's also easy to add additional pieces to the end if the overall size is not big enough; just shape the seam like the other tucks. Starting with a long arc (2, really, for top and bottom) rather than a straight piece would probably reduce the need for tucks, but would also require being close to the correct size and shape from the first cut, as it would be more difficult to adjust.
I like a soft wool for the outer material; it has some give and provides a smooth silhouette. Many people go for cotton, but it can produce sharp creases and puckers which I think detract from the overall look. As for stuffing, while unspun wool seems the most likely candidate for an authentic material, polyester fiberfill is cheap, light, and readily available if you're working on a deadline. It is worth spending a little bit more to get the extra soft stuff, though. Keep in mind that it does have a tendency to poke through most materials if they are not very tightly woven - your particular design will dictate whether this will be a problem or not. Mine will be entirely hidden under the embellishment, so I'm not worried.