I have had fairly close encounters with mental illness (though not personally; at least not in any way that was diagnosed), as I am certain many readers have. In fact, if some recent statistics I have heard about ADHD alone are to be trusted, it would be the odd individual indeed who hadn't had a friend, relative, loved one, colleague etc. diagnosed with some mental illness or another.
The way which most doctors make such diagnoses is by consulting the Diagnostic and Statistical Manual of Mental Disorders. The book, which is being released in a fifth edition this month, is controversial yet is, for better or worse, the standard. For anyone who would like to read about the DSM, Talitha Stevenson wrote an essay reviewing books about the book for the FT in this past weekend's Life and Arts section. Interested readers can find that essay here.