How would I join several pieces of thick plywood together?
Glue and clamp to laminate the plywood together. Just be careful to make sure all the pieces are all well aligned and clamped evenly - use additional wood top and bottom to spread the clamping force evenly and avoid damaging the plywood. Also be mindful that the glue will be squeezed out of the joints so will need to be carefully cleaned off before it dries.