Connect the P-trap to the sink drain tail pipe, by sliding a lock nut and compression washer up and over the tail pipe and tightening the lock nut on the threads of the P-trap.
Install a T-fitting on the other side (outlet side) of the P-trap pipe between the P-trap and the home's main drain pipe. If necessary, cut the existing drain line using a pipe saw. Connect the T-fitting to the drain pipe and P-trap with PVC cement. Note, if your air admittance valve comes with its own T-fitting, meaning is already it connected to a T-fitting, skip this step and simply install it between the P-trap and home's main drain line.
Coat the air admittance valve with PVC cement and push the air admittance valve into the T-fitting.
Allow between 4 and 8 hours of drying time, or as indicated on your PVC cement instructions, before using the drain.