Look at the work of art from a number of different angles. Look at it from close up and from far away. Note the differences in your perception of the work that happen when it is viewed from different perspectives.
Draw a schematic sketch of the basic elements of the work and try to understand the style of composition that the artist was using. For example, in many Renaissance works, artists used a pyramidal effect, with broad and heavy elements at the bottom of the work leading to narrower elements toward the top.
Analyze the colors used in the work. Determine whether the palette used was intended to convey or engender excitement, melancholy, joy or other emotions. Try to understand how the color scheme interacts with the geometric composition.
Familiarize yourself with the artist's other work, and with other work that was being done at the same time, particularly by other artists with whom the maker of your work might have interacted.
Research the place of the work in question in relation to the artist's other work. Determine if it was an early or a late work, if it was commissioned or done privately or if it was done as part of a larger theme or series. If possible, research writings or historical accounts to find out what the artist's opinion of the work was.
Read about the social and political context of the time that the work was made. Many works of art, whether intentionally or unconsciously, reflect the values, priorities and preoccupations of their own period in history.
Learn about the provenance of the work. Find out who owned it, where it resided and any museums, galleries and shows that it was in.
Research the impact of the work of art. Just as it may have been influenced by history, it may have gone on to influence history itself. Look through historical accounts of the time and place where the artwork first appeared to learn about the reactions of the public at the time.
Find out about the current status of the work of art: where it is held, what other writers have written about it and whether its reputation has changed significantly since the time that it was made.