Pull down the existing soft tiles from the suspended frame by pushing them up into the space above the frame and tilting them until one corner drops out of it. The rest of the tile can then be pulled down.
Buy acoustic tiles that will fit into your suspended ceiling. Most ceilings use 2-by-4-foot tiles, but some use 2-by-2s to avoid an institutional look. Acoustic tiles are made of materials that increase sound absorption and reduce the sound transmission through the ceiling.
Cut the acoustic tiles with a saw, if necessary, to fit them in an odd-sized ceiling grid.
Place all of the tiles into the grid by tilting them slightly and sliding them into the space above it, then letting them settle onto the metal grid frame.
Remove the existing ceiling tiles, then use a drill to remove the screws holding up the metal grid that held them. Pull it down from the ceiling.
Attach soundproof vinyl sheeting to the wooden ceiling joists with roofing nails hammered through plastic washers. This sheeting is heavy, so it may need to be cut into pieces for easy installation. This sheeting is available at most home improvement stores.
Cover all the seams between pieces of vinyl with barrier tape, available where you bought the sheeting.
Seal any cracks with acoustic sealant, also available from any hardware store. Pay close attention to the cracks between the ceiling and the walls. Even a small gap will admit substantial amounts of sound.
Reattach the metal suspended ceiling and put the tiles back into place. For optimal soundproofing, use acoustic tiles as well as vinyl sheeting.