I'm no expert, and I didn't have a slope or creek to drain into. My primary concern was to give water/rain someplace to drain so it can eventually be absorbed into the soil, without causing a muddy mess in the run in the mean time.
My "duck house" is about 8'x15', and here's what I did:
I used a concrete perimeter foundation, and dug out the entire inside after the concrete set up. Then, I laid down a layer of landscaping cloth:
Then I laid down a couple of inches of gravel, followed by some perforated PVC tubing of the same type used for French drains. Obviously, the tubing won't drain the water anywhere, but it added some empty air pockets in the gravel that can fill with water until it can be absorbed by the ground:
Then, I covered all the PVC with more gravel:
Then, I added another layer of landscaping cloth and finished it off with sand:
I've only got 3 Muscovies, and they only have the small pond visible in the photos, and some drinking water. But the sides of the run are pretty open, and the roof will only provide so much protection from rain... But, so far so good. The sand doesn't stay completely dry, obviously, but I haven't had any puddles form, and no swampy areas, despite having had alot of rain recently.