Typically they are made of leather, wood or other plant material, and often consist of multiple parts for better durability of the sole, stitched to a leather upper.
Typically a shoemaker uses a last to form the shoe on. Traditionally it has been made of either iron or wood, and can be straight, or used exclusively for left or right shoes.
The profession of shoemaking has had its own stories (Shoemaker's elves), patron saint (Saint Crispin), and proverbs ("The shoemaker's children are often shoeless").
Some types of ancient and traditionally-made shoes:
Romans fighting in northern Europe: furs wrapped around feet, and sandals wrapped over them
Clogs: wooden shoes, often filled with straw to warm the feet
Mocassins: simple shoes, often without the durability of joined shoes (although different types of leather have different wear characteristics)
The SCA offers some advice about making period shoes.
Current crafters often use used car tire tread as a cheap alternative to creating soles.
Shoemaking and Tailoring in Civil War Winter Quarters
A number of shoemakers in the different regiments, seventeen I think, were encouraged to send home--and in some instances were given leave to go--for their tools, and were put to work repairing shoes, being exempted from guard and other routine camp duty, but ready to fall in with their commands on any call to arms.
The shoe-shops were a separate camp of tents, near brigade headquarters and under our immediate supervision, guarded by sentinels, and no person was allowed to visit them or to carry his shoes to be mended without a pass and order from his company and regimental commanders, approved by the adjutant or inspector general.