I have hunted upland game and waterfowl on reservations in South Dakota - which is pretty straight forward. Keep in mind that regulations will vary (in some cases quit a bit) depending amoung the different reservations.

Big game can be trickier, you just have to make sure you know the rules and regs of the reservations that you are planning to hunt. If I was going to book a hunt through an outfitter on a reservation, I would probably call and/or email the ribal headquarters and verify everything was in the right...

BTW - Personally, I don't think I would be doing ANY type of hunting on the Pine Ridge Res. That one is generally considered the roughest in the state.