Slip one end of a PVC tube onto the end of the P-trap under the sink. Turn the nut on the tube clockwise to connect it with the P-trap.
Connect a T-fitting to the other side of the PVC tube, so that the two openings on the T-fitting point up and down.
Place another section of PVC pipe into the bottom of the T-fitting and run the pipe to the drain pipe, which is likely located under the floor. You may have to use a 2-inch hole saw to cut through the floor to access the drain pipe.
Place a 12-inch section of PVC pipe into the top of the T-fitting, followed by a 45-degree fitting. Place a 6-inch section of PVC pipe into the 45-degree fitting, followed by another 45-degree fitting. Place one more section of 6-inch PVC pipe into the fitting and then attach one last 45-degree fitting to that pipe. When completed, the pipe will have bent 180 degrees and is not parallel to the T-fitting.
Insert a section of PVC pipe into the last of the 45-degree fittings that is long enough to reach the vent stack pipe under the floor. Again, you may need to drill a 2-inch hole through the floor to access the vent stack pipe.
Connect the PVC pipe to the vent stack by inserting the pipe into a clean-out plug or other opening along the pipe, and securing with a PVC solvent fitting. Swab the fitting with PVC cement prior to fitting over the vent stack pipe. The loop is now connected to both the drain and the vent stack.