If you're setting your shed on something that's ABOVE ground, you needn't dig for any reason. The downside to setting a shed on, say, a few concrete pavers at the corners is that eventually they'll sink. This is not desireable. Forget the idea. Now ...
You want to prevent sinking but you don't want to have to go through the trouble of putting in concrete footings. In a case where you want to dig down to fill a hole with gravel or with concrete, you need to find the frost line and dig another foot or so. This is for drainage and to help prevent 'upheavel'. If you choose to use gravel, line the ditch with 2 or 3 layers of filter fabric. NOT landscape fabric. (A gravel yard will have this stuff.) THEN put in your stone. (Basically, you're wrapping your stone in fabic to prevent dirt from contaminating your gravel.) My 12' x 16' shed has five (5) 4" x 4" pressure treated rails under it. They run along the 16' dimension. The front and rear have a rail and the other 3 are evenly spaced in between them. You want to do the same thing with your shed if you don't already have rails. Mine are 3' apart on center. By putting on rails, you keep the shed off the ground and allow air to flow underneath. This keeps the shed floor dry, hence, a longer lasting shed.
By having a 4" x 4" rail 'at each corner' (in principle), your gravel hole should be 14" wide, or more. That's 6" on each side in case the shed moves on you. The gravel should be filled 2" at a time and TAMPED down with a tamper. Use 3/4" drywell gravel. Don't put in 3" and tamp; do 2" at a time. Don't hurry this job if you want to get out the 'cheaper' way. Fill the hole up to the point where you can set in your concrete paver. Then, you're done! Now, are you ready for the bad news?! The weight of the shed will probably split the concrete paver! Unless you have something stronger, this is a risk you take. You can take your chances and simply fill the hole to the top with just gravel and set your shed-rails on it. But the problem is, you're gonna get settling. Eventually, your shed rails will, well, sit on the ground.
'Noname' suggests you should use poured posts. You can use gravel but what I suggest you do is build a 10' x 10' wide pit that's 6" deep and line it with 2 rows of 4" x 4" pressure treated lumber rated for BELOW-GROUND use. Make sure you have good drainage in the pit. (Dig out the lowest corner to let the water run out.) Attach the lumber to each other all the way around with galvanized nails (pre-drill first). Line the pit with landscape fabric (not filter fabric). Fill with 6" of stone, 2" at a time while tamping it. Set your shed (already on rails) right on top, and you're done! Poured concrete posts are the best. Just follow my aforementioned instructions for putting gravel in a hole except use concrete. (Make sure you put 6" of gravel in the pit, before you pour, for drainage. Again, dig at least 1' below frost line!)
My best to ya and hope this helps.
PS: If you go the route of using 4 x 4 lumber to line the pit, buy 4 extra pieces. You see, when you lay an 8' 4 x 4 next to another one, you need to 'center' an 8' 4 x 4 on top of it so you can attach it. If you take a few minutes to draw it out on a piece of paper, you'll see that you'll have to cut up a few boards, hence, waste a few pieces in the process. If you end up having any difficulty with envisioning this, I can help you. Just e-mail me directly.