How does the doctor diagnose pink eye?

Several ways. Usually this is a clinical diagnosis it is based on the history given, the symptoms, the examination of the eye (s) the type of discharge, and other historical and exam findings. There are some rapid tests to determine if the infection is viral or bacterial. One can also do a smear of the discharge and stain it and determine the type by looking at the slide. Culture can be taken too!
Examining. The conjunctiva for little bumps called papillae and follicles, and asking some questions. Rarely need to send culture.

Related Questions

How does a doctor diagnose pink eye? Or what kind of test do they do to find out if you have pink eye?

No testing needed. Conjunctivitis, aka pink-eye, is referred to acute superficial infection of the eye (s), either viral or bacterial cause. Viral infection typically produces redness, watery eyes and does not need treatment except for herpes. Bacterial pink-eye causes redness and purulent discharge (puss), often "matting the lids/lashes together" in the am or after long nap. Consult doc if you have it. Good luck.
Clinical diagnosis. It is a clinical diagnosis based on history and examination. No specific test needed.