Knitting caps is not very difficult. Beyond the basics of the stocking stitch, one needs to know how to knit in the round (using 4 or 5 double pointed needles) and to increase and decrease. All the caps shown below are variations of these techniques. I've seen descriptions for knitting caps starting at the bottom (brim) or at the top (crown). There is no difinitive evidence one way or the other and caps were probably knit with both methods.
The Monmouth cap was a common item in England around the second half of the 16th century. It was, in fact, so common that no one saw fit to leave a good description of the cap for us to find. The term 'Monmouth cap' may have referred to a specific type of hat or to knitted caps in general from the area surrounding Monmouth, England. From loose descriptions and two trade tokens from 1656 and 1670, we are left with very few distinguishable features.
However, there is one extant cap which may be a genuine Monmouth cap.
There is an excellent article written for Costume (Volume 13, 1979) by Mrs. Kristie Buckland which compiles all the known evidence for these caps. In it, she describes how the one remaining cap is made:
From literary references of the time, it appears that such a cap would be a reasonable item for a middle class English persona with military connections to own. It is practical to keep one's head warm in winter and to keep the foul humors out. And such a common item would not be out of place.
Also see The Monmouth Cap Page for more information and pictures.
Usually mentioned in refference to sailors, this cap is similar in shape to the Monmouth, but is characterized by a fuzzy appearance. The best description of this I have heard is from "17th Century Knitting Patterns - As Adapted for Plimoth Plantation". Scraps of yarn and wool are tied to the finished knit cap for extra warmth and protection from weather. These caps were likely felted as well.Check out the thrum on this seaman from Habiti Antichi e Moderni by Cesare Vecelli, 1600. (Tincey, p 22)
Marion McNealy has an excellent pattern derrived from finds on a wreck from 1583.
See this newslist archive for a complete pattern and nice bibliography.
These caps were fairly common and can be seen in several portraits. A similar style of hat (sometimes called a bonnet) was made in a similar shape out of a stiffened form (probably felt) covered with cloth. Janet Arnold kindly details this type of hat in Patterns of Fashion. For more pictures of bonnets and flat caps, see Dawn's Costume Guide to the Tudor Cap.