The baby has a little bit of discharge near his eyes constantly, like …

The baby has a little bit of discharge near his eyes constantly, like conjunctivitis. I know it's from water. It's bad and I suffer from it too but how can I help the baby? And generally, how is the best way to maintain facial hygiene for a month-old baby? I just wipe with water carefully, but I don't know how to do it right. Please tell me.