The tear duct sits at the inner corner of the eye, just beside the bridge of the nose. Feel for the small bony bump there.
This is primarily used for blocked oil glands (Chalazion/Stye) but can help general drainage.
Stop massage and seek professional medical care if you notice:
When this duct is blocked, tears back up into the sac, causing swelling and discharge. The goal of the massage is to create hydrostatic pressure to push the fluid through the blockage or "pop" open a membranous obstruction.
To perform the massage correctly, it helps to visualize the tear drainage system:

