There are several options for soundproofing depending on the depth of the cavity between your joists. These include flexible membranes, Roxul insulation, XPS board, 5/8" drywall, Green Glue, resilient channel, or some combination of these materials. The keys are to add mass/density, and/or interrupt the transmission of sound through structural members using "space". There are some good online resources to help create adequate soundproofing for your situation. Good luck!

Best way to soundproof a ceiling is. 1) Insulate the cavity between your ceiling joist with Mineral Wool or Fiberglass. 2) install sound resilient clips, furring channels onto the ceiling joists (that will add tremendously for impact too) . 3) Apply drywall and screw into the channels. 4) add Green Glue Damping Compound and another layer of drywall. 5) Caulk the perimeter using high quality Acoustical Caulk, additionally caulk the space between the recessed lighting and the drywall.

Is that the way to do THIS ceiling?

glance, can you be more specific in what you mean "sound proof"? Do you mean to stop sound from transmitting to an adjacent space? Or do you mean to acoustically treat the surface so the sound system sounds better in the room?

This ceiling is complicated as it looks like they want to have an exposed beam look in the room. In that case proper soundproofing is not really possible. Best they can do is add a 2nd layer of drywall with the GG Damping Compound in between the joists.