There were many types of footwear worn in period, with different types of construction. For people wearing outfits from before about 1500 what we call 'Turned Shoes' were the most commonly worn, especially among the social classes generally presented by the SCA. For people wearing outfits set after 1500, the most commonly worn sort of shoe was what we today call 'Welted Shoes'.
Turned shoes were single-sole shoes that to modern sensibilities often seem like slippers or moccasins, and are therefore dismissed. They were made inside out, then turned right-side out. These were frequently made on a last (or a specially carved wooden form), especially after the 1200s, although a last is not always required. Some later period shoes were given added outer soles that helped them last longer.
Welted shoes were made in a more modern fashion, right-side out, on a last. Separate raised heels are not found until after 1600 (except in some rare occurrences regarding carved wooden or cork soles in the 16th century).
Shoemakers (or Cordwainers) and Cobblers are not the same thing. Shoemakers were required to work in new leather, while Cobblers were required to work in old, used leather. There were serious class distinctions between the two.
Overshoes called pattens were made of wood with a leather strap or leather and cork (somewhat like a modern Berkeinstock).
Footwear of the Middle ages - http://www.personal.utulsa.edu/~marc-carlson/shoe/SHOEHOME.HTM (there are more extensive links there)