Contact your local building authority to learn the building code rules for this type of project, and procure the necessary permits.
Consult with a qualified HVAC technician to understand the right locations, paths and sizes of return ducts that will improve the heat distribution of the forced air system.
Put on leather work gloves and safety glasses.
Cut the existing drywall with a utility knife in the locations recommend by the HVAC technician for the new return vents. Pull the drywall off the wall by hammering holes in it and using the holes to pull it off the wall studs with your hands.
Drill a 3/4-inch hole through the center of the wall bottom plates in the locations that need to be penetrated to run the returns between floors. Cut the bottom plate out using a reciprocating saw starting in the hole drilled.
Install a return-vent duct bracket between the wood joists in the location of the return vent. Fasten it to the wood framing on either side with the proper screws.
Connect ducting material from the underside of wall/floor, where the return penetrates the bottom plate, toward the existing return-duct system. Duct work sections are connected by pushing the male end in to the female end and securing with several self-tapping screws through the joint.
Secure the duct work to the basement ceiling with duct work hanger brackets. One side of the bracket fastens to the duct work with a self-tapping screw, and the other end fastens to the wood joist with a wood screw.
Connect the new return duct work to the existing return plenum. Cut a hole in the existing plenum with tin snips, then fasten the duct work together with self-tapping screws.
Reinstall drywall over the removed sections. Apply drywall joint compound to the drywall joints and allow to dry overnight. Sand the drywall joint compound smooth and paint to match the existing wall color.
Install a return vent grille onto the vent bracket with one screw through either side of the cover and into the bracket.
Contact your local building authority to inspect your installation before turning the furnace back on.