Install ceiling insulation. Ceiling insulation creates a substantial sound buffer between your apartment and the upstairs apartment. If the apartment is under construction, you can add the insulation before the drywall goes up. Insulation can also be blown in to an already existing ceiling.
Use flexible ductwork in the ceiling, if possible. Sound travels better through a straight line, making flexible ductwork a better option to decrease sound between the floors.
Caulk around any registers or vents in the ceiling. Just as air can seep through the space around registers and vents, so can sound.
Install carpeting on the floor in the upstairs apartment, if this is an option. Carpeted floors transmit significantly less noise than vinyl, tile or hardwood floors.
Install acoustic ceiling tiles. Acoustic ceiling tiles essentially create a dropped-down ceiling made from tiles that are designed to reduce noise transmission from above.