I wandered into one quite by accident once, going to shoot some clays at an open-to-the-public clays/trap/skeet place in a state where pigeon shoots are legal. It was a quiet afternoon when all the other shooters had already finished and gone home. I was allowed to and did hang out and kinda watched - from a great distance - and wanted no part of it for two reasons. Actually three.
First, the shooters seemed to be wounding a lot of birds and that meant wounded pigeons were fluttering down all over the place, being policed up by a couple youngish folks.
Second, the folks doing the shooting seemed to be the kind of folks for whom killing was the objective. You probably know what I mean - and their consciousness was not appealing to me, so I didn't want to be around them.
Third, it seemed to me that this was a big-money deal, both in terms of getting in (i.e., paying for the birds, etc.) and probably the side betting that was probably going on quietly off in the corners. I have no appetite for either.
Management at the place seemed a little embarrassed by the whole thing, but I suppose they were willing to stomach any discomfort b/c these were paying customers.
But, to come back to the lead poster's basic question: you won't find these advertised let alone on the internet, you almost certainly need an invitation to go and shoot and you'll only get one if you'll fit in with that crowd, and be prepared to cough up a lot of coin for the privilege. Kind of like getting to be a member of the club at Augusta or something similar - you can't seek an invite (if you do, you'll never get one) and if you do any answer other than "where do I send the check and how much?" will likely get you blackballed.