First, build the frame taller than the wind can reach, then angle the walls back a bit so the wind runs off them. Tighten every seam with rope or tape, and bolt the corners to the ground or use metal stakes to keep the frame from shifting. Add a layer of canvas or tarp over the whole thing and seal the edges with a waterproof sealant or even a layer of mud at the base. Keep a small pile of sand or rocks against the windward side to add weight and stop any sudden gusts from blowing the walls loose. If you do that, the shelter should stay dry for a long time.

Good point about the corners, that’s where most of the weak spots are. Stone’s a solid choice, just make sure it’s firmly packed so the wind can’t pry it loose. Keep an eye on those seams, though; even a small gap will let a breeze in and wet the whole thing up. Stay on it and you’ll have a dry camp for a while.