Concrete shed foundations vary in thickness, depending on the size and weight of the shed and the soil conditions, local climate and use of the shed. A large shed used to store lawn tractors and similar heavy equipment will need a thicker slab than a small potting shed. A slab on good, firm soil may be thinner than one on sandy or less stable ground. A slab subject to severe winters with heavy snow loads and constant freezing and thawing will be different from one installed in a location in a warm climate.
The base under a slab is often more important than the depth of the slab itself. Slabs should be built on a base of compacted gravel over firm, compacted soil. The depth of that gravel base --- and the size of the gravel used --- will vary by locale. Local building codes often regulate the size of the base, depending on the "frost line," or level of ground subject to freezing and thawing, which can create movement and causing cracking in a slab.
A 4-inch slab is generally a good thickness for a typical shed. This concrete floor can be poured in most locales on a 4-inch base of compacted gravel. That requires an excavation of at least 6 inches to make a slab that will be 2 inches above the surrounding ground. This slab would use forms made of 2-inch by 4-inch framing lumber that are set on top of the compacted gravel.
A 4-inch slab can be strengthened by putting a layer of steel wire inside the form for reinforcing. A thicker slab can be made with a 6-inch gravel base and 2-inch by 6-inch forms for a 6-inch slab if you're building a shed that will be subjected to heavier weights. It's a good idea to add a perimeter trench an inch or so deeper than the main slab area around the outside edges. Adding extra gravel and concrete at the perimeter will make a firmer base for the shed walls.