Loosen the large nut on the sink drain’s bottom with a pipe wrench. Pull the drainpipe from the sink’s bottom and rotate it slightly to one side.
Measure the T-pipe length that came with the air vent with a measuring tape. Locate the sink drainpipe’s horizontal section. Cut a section the same dimension as the T-pipe from the drainpipe’s horizontal part with a hack saw. Remove and discard the section. Clean the burrs from each end of the drainpipe with very coarse sandpaper.
Slide slip-joint nuts with the threads facing the pipe’s cut end over each end of the drainpipe. Slide slip-joint washers over each pipes’ ends up to the nuts. Wrap thee T-pipe threads with three wraps of plumber’s tape. Slide each cut drainpipe end into each side of the T-pipe. Rotate the T-pipe so that the fitting faces upwards. Tighten the slip-joint nuts with pliers.
Wrap three wraps of plumber’s tape around the air vent’s threads. Thread the air vent onto the fitting on top of the T-pipe hand tight.
Rotate the drainpipe slightly, so that it lines up with the drain on the sink’s underside. Tighten the fitting on the drain with a pipe wrench. Fill the sink with water and let it drain. Check all connections for leaks and tighten the connections if necessary.