He used 1 x 6 Pine boards to first conceal the damage done midway where the wall partition was. Then he calculated out the measurements to evenly distribute the framing that would form the grid. Scraps of 2 x 4 regular boards and other things were installed directly to the ceiling to provide him with a backing to nail the new lowered ceiling onto. I'm typing this as best as I can describe it because it just comes automatic to him how to build these structures.
He used a Finishing Air nailer and 2" finishing nails along with a mitre saw for precise cuts.