There are two popular routes: "W" (shorter) and "O" (longer). Camping is allowed only in official spots. All accommodation has to be booked in advance, it is strictly enforced, otherwise you won't be allowed to enter the park.
There are three companies providing camping sites and accommodation: CONAF (governmental), Fantastico Sur and Vertice.
Lifehack: book "Chileno" camp site first, since it tends to be very busy, adjust the rest of the tour to that.