Generally speaking, a mental illness has two parts – 1. a collection of symptoms and signs, 2. disturbance of functioning and suffering to the person. For each symptom, a psychiatrist see how persistent and prominent it is and how it is accompanied by other symptoms. For example, in a depressive illness, the mood is markedly depressed for most of the time of the day, lasting for more than 2 weeks and accompanied by other symptoms like loss of energy and interest. These symptoms impair the functioning of the person, e.g. lower his performance at work. All in all, defining abnormality in a mental activity demands clinical experience and skills of a doctor, and therefore, assessment by a doctor is indicated when a mental illness is suspected. 

You can refer to the following website.

How does a psychiatrist diagnose mental illness?

The source of information is provided by the Hospital Authority Castle Peak Hospital