The previous owners left us with a 9x12' slab they had poured for a
dog kennel; it happens to be in the same place I want to build a shed.
The slab is 7" deep and though it's an obvious DIY job it has held up
for 10+ Minnesota winters. Assuming I want to build an 8x12 shed on
PT sills atop this slab, what's the best way to anchor the sills?

First, if the slab is 9x12, it would be best to build a 9x12 shed so the
siding can overlap the edge of the slab. Otherwise, rain water is going to
run down the sides of the wall, hit the slab, and go under the wall into
the shed.

As for anchoring, the only real option you have is to drill through the
sill and into the concrete slab with a masonry bit. Then install expanding
anchor bolts and a large washer. The more bolts you install, the more
secure the shed will be to the slab. You can usually find these "retrofit"
anchor bolts in the same area as regular anchor bolts and framing brackets
in the home centers. But regular expanding anchor bolts are essentially the
same thing. I'd select 3/8" or 1/2" bolts, as long as you can fit in the
slab (don't drill all the way through the slab).

Remember the sill is only part of the building. You'll need to nail the
sheathing every 6" to tie the sill, studs, and plates together. You should
also use "hurricane" straps on the rafters.

It's probably overkill for a shed, but this is standard building practice,
and the costs are minimal so why not...

Anthony