The classification and diagnosis of psychiatric disorders are guided by two major classification systems- the International Classification of Diseases (ICD), published by the World Health Organisation (WHO) and the Diagnostic and Statistical Manual of Mental Disorders (DSM), published by the American Psychiatric Association.
The DSM is to be released next month in its 5th edition. With each edition, there have been various changes and additions to diagnostic criteria and categories. The DSM has received a huge amount of criticism from multiple sources and for various reasons. I would probably pass out from typing fatigue if I tried to comprehensively summarise this area. Instead, I'll be lazy and point you towards a couple of sources I have found to be an interesting general read about the DSM:
One of the big changes to come in the 5th edition is a move towards 'dimensional' rather than 'categorical' measures of disorders. In a nutshell, the categorical approach is one where you either have or don't have a particular diagnosis- you have a depressive disorder or you do not. The problem with this is that the real world is much grayer and blurry than this. In reality, people suffer from different symptoms at different severity levels. This means that two people with the same diagnosis can look quite different from each other (in terms of the way this problem shows itself). A dimensional approach is one that focuses less on an in/out diagnostic label, and more on the fact that human behaviour and characteristics exist on a continuum. This means there is wide variation in how much a particular characteristic is displayed. For instance, some people outwardly display very little anger, while others are basically constantly erupting towers of rage. A dimensional approach places more importance on the extent to which a particular problem/characteristic is present in an individual. For instance, instead of focusing on the diagnosis of depression, there is emphasis on a 'moderate' level of low mood, 'severe' sleep disturbance, 'mild' social withdrawal. A lot of people like this approach because it focuses more on individual differences in the actual experience of mental health problems.
In my own experience working with people, I have become more in favour of describing the set of issues a person is experiencing, rather than on making a 'diagnosis'. This is a good way to try and help a person make sense of how individual problems/symptom occur, and how they might relate to each other. For instance, lack of sleep is a common problem in people suffering from depression. Low energy levels and difficulty concentrating can also occur with low mood, and these may be a consequence of sleep disturbance.
Having said this about a dimensional approach, some people want to have a name attached to their problems. Sometimes this reduces any self-blame that may have been occurring and/or dampens down the fear that he/she has gone 'crazy' (lost one's own marbles, etc....). Also, this can be a helpful short-hand way of taking about a set of difficulties that tend to occur in combination. In practice, I tend to try and work in with people's preferences and I think there are potential benefits of both categorical and dimensional approaches.
Mental health professionals have to be very careful about the whole diagnosis process. It potentially puts professionals in a very powerful position for all sorts of reasons. In some settings, it is a necessary part of working with the health system (e.g., diagnosis is often needed to access particular resources and support). Despite this, we should be careful that this does not become our sole way of describing or thinking about a person. It can be easy to fall into this trap when working in a setting where the emphasis is on putting people into categories.