There are various ways to soundproof an existing ceiling. The most common way is diagrammed below:
"Best": This is the most effective solution to eliminating noise from above your ceiling. This is one solution to get the most noise loss from upstairs. It uses our Sound Barrier, MLV Tape, Sound Insul, and Sound Clips or NE Clip System on top of your existing ceiling to eliminate the transmission and airborne noise coming from above.
This is the most common procedures for existing ceiling soundproofing, there are other procedures available, call for more details.