How to Read a Photograph

When reading a photograph, you look at the 'photographic discourse' to find the meaning of the image and what the photographer has done to achieve this.
This involves looking at the denotative and conotative  meanings in the photograph.
Denotative - the literal meaning and details in the image.
Conotative - the deeper meaning of elements in the image; how they reflect certain attitudes or expressions in society and what they are used to represent.

Roland Barthes introduced the concept of studium and punctum in his book Camera Lucida.
Studium - looking the cultural, linguistic and political interpretation of the image, the literal meaning (denotative).
Punctum - the deeper, personally touching details and meaning (conotative).

It is also important to research the social, economic, and political factors at the time the photograph was taken in order to achieve a broader analysis.

"A Family on Their Lawn One Sunday in Westchester, New York" - Arbus 1969

My Interpretation
Studium - The photograph shows a family in their garden. The two parents are relaxing while their child plays by their self behind them. In terms of composition, Arbus has used the 'rule of thirds' technique in order to draw attention to the parents - making them the focus of the image as they are placed at the intersections of an imaginary grid that splits the frame into thirds from top to bottom and from left to right. Additionally, the upper third of the frame is taken over by the forest which appears to be very dark and intimidating due to the low exposure that Arbus used.

Punctum - You would imagine that with such a large garden the family would be wealthy and therefore happy; however as our eyes are drawn to the focus points of the wife and husband we see a contradiction to this. On one hand, the wife looks very relaxed and content with her arms stretched out and her eyes closed. The man, on the other hand, appears to be frustrated or concerned as he is covering his face with his hand - which is often a sign of despair or worriedness. Finally, there is the child playing behind the parents alone that creates a sense of neglect and loneliness. This leads me to think that the family are, in fact, not happy.
The idea of the 'American dream' comes to mind when I look at this image. This is a goal that is achieved by having a good job (traditionally by owning your own business), to be able to afford a large house and comfortably finance a happy family - something that was particularly popular in the 1960's. This leads me to think that the husband in the photograph is facing issues with money that his wife is oblivious to - and these troubles are represented by the dark, looming forest behind them.