The Amazon tour is connected to the lodge where you stay. There are a few hotels in Puerto Maldonado itself, but if you're going all that way, I think you'd want to stay at one of the river lodges. They're all-inclusive, usually minus the cost of alcoholic beverages. You'll land at Puerto Maldonado airport, and a lodge representative will greet you with a sign. You'll be taken to the river docks in town and off you go on the river to your lodge, a boat ride of anywhere from 30 minutes to a few hours. You'll stay at your lodge however many days you've booked. The stay will include meals and guided tours. When you leave, they bring you back via river to town and to the airport.

So, obviously, this has to all be arranged in advance. There's no way logistically to simply show up at these places. Several lodges, different comfort levels, ... A guidebook will help you sort through the choices.

Remember, you're not going to see the Amazon River itself. These are tributaries of the Amazon river, the Madre de Dios or Tambopata rivers. You'll be able to say you've seen the Amazon basin. It's still beautiful and impressive.