Best bet is to stay in either Durango or Pagosa Springs. Largely a hike-in stream, the Piedra has two gravel road accesses from both the east and west sides. The east side road runs upstream for twelve miles. Several trails reach the river from the road. Fishable year-round but best from summer to late fall.
Water can become murky easily.
Great place for a multi-piece rod since you'll likely be hiking a good bit. I wade wet with neoprene socks and felt-soled wading boots. Friends pack in lightweight breathable waders but since you scramble on rocks and hike and such, you've got to be careful not to tear them up. Bag and possession limit is two trout. Wild brown and rainbow trout averaging 12 inches, with many larger fish.