Recently a friend asked me how he should look at a painting; and what could he do, to understand what the artist is trying to say. We are, of course, speaking of abstract or what in common parlance is termed 'modern art'. I gave him my standard reply, "Just look at it and see what it evokes in you." What the artist wants to say is not quite so important as what is actually being said to you, in other words, whatever it is that you are receiving from the painting.
Yet, he persisted, so I gave him an introductory book on 'Understanding Art'. It delineates the basic movements in art history - Early Renaissance, High Renaissance, Baroque, High Baroque, Rococo, Neo-Classicism, Romanticism, Realism, Impressionism, Expressionism, Symbolism, Cubism, Futurism, Dada, Surrealism, Abstraction and so on. It also speaks of how certain artists improvised the methods of artistic expression and changed the course of art history.
However, I still maintain my earlier position that a work of art speaks to the viewer in the moment of its perception. The artwork carries within it the feelings and thoughts that the artist had as s/he created the painting. When we perceive the painting without any preconceptions or even any desire to understand/interpret it, we directly apprehend, perhaps at a subliminal level, those thoughts and feelings. And even if we don't 'get it', we are richer for the experience.
The ancient Indian theory of Rasa speaks of the dynamic relationship between the art-viewer and the artwork. It might be dance or classical music or any other art form, including paintings. Although, Abhinavadarpan and Bharata's Natyashastra deal mainly with drama, they do delineate the aesthetic contentions of the Indian philosophy. The theory asserts that the essence-juice (poor translation of Rasa!) or 'the Capturing the very essence, the very spirit of something, in order to evoke a specific mood or emotion in the viewer's brain' (a better translation of the term) of the art is a product of the act of perception as much as it is of the act of creation. Thus, the artist and the viewer have an almost equal responsibility in art appreciation.
Coming back to a layman's approach to art appreciation - if you are just not able to go beyond the world of words, then another way of viewing a painting would be to identify the central theme of the painting and to put it in one word. Then, one can look at all the elements in the painting and see how they reflect and/or enhance that central theme. It does not matter, whether the artist intended that as their central theme or not. The exercise is to help one to look deeply at the painting, see the relationships between the various elements in the painting and to see how they are tied together thematically. A commercial on television for IBM depicts this rather graphically. A couple of professionals are looking at a work of art and reading into it all kinds of things that liken it to their organization and seeing complex things like the supply and demand chain, the networking etc. whereas another onlooker, who joins them, simply comments that it looks like a horse to him.
As a psychologist I feel that every work of art is to some extent a Rorschach's inkblot. It is a projective tool that allows you to project your thoughts and feelings on to it. The intriguing patterns and colors are aids to evoke emotions and attract different responses. You might say 'then why not put an empty canvas' and there are artists who do just that. Anyhow, the point is that viewing a painting is as much an invitation to self-awareness, as it is an invitation into the mental and emotional processes of the artist.
But, if we really want to understand the latter then we need to look at the painting while keeping in mind the context in which it was created. What were the trends in art until then, what was the socio-cultural milieu prevalent at the time, what phase of life was the artist going through, what were the concerns s/he was preoccupied with, and so on and so forth.