I have a 3 week old baby with a cold in his eye with greenish drainage. What can I do to clear this up?

Wipe it away. The normal drainage path for tears is a tear sac & tiny channel down the inside of the nose. It blocks easily when debris from allergies, viruses or other germs.Newborns often have ducts that are blocked for the first months until head growth helps them open.If simple goop & no lid redness u can tease it away with a clean cloth.Progressive lid redness may require a visit & meds.