[dmun]

Generally speaking, once you start installing utilities, you need a permit.
The actual rule, from memory, is less than 50 square feet, less than 10 feet tall, no utilities: no permit. It's a shed exemption, which also covers things like backyard barbeques and pizza ovens.

For the foundation, either one of two things. Either you pour a slab on a base of well drained crushed rock, where the structure in essense floats over the soil, or you dig down below the frost line and pour footings directly on the undisturbed sub-soil. If you do footings, it's only around the edge, the whole slab doesn't need to be that thick.

And I second RT's suggestion, that if you're using a contractor, you want the inspection before you make the final payment. That's the law here, and it's for your protection.