Attach a PVC coupling onto the end of the sink's P-trap pipe by threading it onto the pipe. This is the vertical pipe extending back from the P-trap.
Install a T-fitting onto the top of the vertical drain pipe in your island sink. This pipe connects to the main drain line in the home. Measure the distance from the end of the coupling on the P-trap pipe to the T-fitting with a tape measure.
Cut a length of pipe to meet the measurement in Step 2 with a hack saw. Install the pipe between the T-fitting and the coupling. Insert the air admittance valve on top of the T-fitting. If the valve does not fit, trim down the vertical drain pipe with a hacksaw.
Disassemble the pipes and couplings. Coat all of the edges with PVC adhesive and reassemble the couplings, pipes and vent. Let this installation dry for four to eight hours or as advised by the PVC cement instructions.