Install 2 × 6 blocking between the wall studs, behind the planned sink location where you will drive screws to mount the sink. Cover the wall with water-resistant drywall. Waste and supply lines may need to be moved, depending on the sink.
Set the basin and pedestal in position and brace it with 2 × 4s. Outline the top of the basin on the wall, and mark the base of the pedestal on the floor. Mark reference points on the wall and floor through the mounting holes found on the back of the sink and the bottom of the pedestal.
Set aside the basin and pedestal. Drill pilot holes in the wall and floor at the reference points, then reposition the pedestal. Anchor the pedestal to the floor with lag screws.
Attach the faucet, then set the sink on the pedestal. Align the holes in the back of the sink with the pilot holes drilled in the wall, then drive lag screws and washers into the wall brace using a ratchet wrench. Do not overtighten the screws.
Hook up the drain and supply fittings. Caulk between the back of the sink and the wall when installation is finished. You may choose to apply caulk between the sink and the wall, or between the bottom of the pedestal and the floor.