Depends on the conditions, but typically I catch them in the "entrance" to the hut. It's a deep channel leading inside the hut. It's the deepest water next to the hut that's usually the most productive. But I've caught fish in the shallow areas as well.
I usually start by fishing spinnerbaits and topwaters around the outer edges, then work my way in with T-rigged plastics, Senkos, and jigs. And once I feel I've caught them all, I go back to the spinnerbait. I'm still surprised when I catch a few more on spinnerbaits and then go through the whole process all over again, picking off more fish.
It's like it replenishes. You just have to be patient and realize some fish will hit reaction baits while others hit slower-moving baits. Just keep changing baits/presentations when the bite slows down...even going back to previous baits.
It's not like you've caught them all. You've only caught the ones that were there at that time....and more moved in as the ones you caught moved out.
I've been known to sit on huts for an hour or more, picking off fish every 5-10 mins. Muskrat huts too.