I just moved into a one year old home. The old owners planted a jap. Maple too close to the house. How deep would the root system be? And when is the best time of the year to transplant it?

Don't worry about getting all the roots. Depending how big the tree is, going down a foot or 2 should be enough. It is more important to limit the root ball to what you can handle and not crack it. A good guide line is to go to a nursery and look at the balls on similar sized trees. Try to find real balled and burlapped trees. Many of the trees were shipped bare root and planted in potting soil in containers that may not really show how big the roots are. If you are not moving the tree very far or handling it much, you may not have to burlap it, but be very careful not to crack the root ball.

Commercial landscapers work most of the year. Still, fall is the best time of the year. Even then, it can be dry, and require water. Do not let the tree go into winter dry.