In many ways, we interpret art the way we interpret literature. If you have ever done any literary analysis at all, think about how you approach it. You look for themes in the work, and then you look for evidence to support the themes you see, symbols, the setting, characters, the author's use of words, and so on. Themes are ideas, and a work of art has themes, too. What does the artist want you to take away after looking at the work of art? Another way to look at this is to think of a work of art telling a story. What story is the artist telling? What does he or she use to tell the story?
Let me give you an example. There is a famous painting by Jean-Francois Millet called "The Man with the Hoe." I have provided a link to it below. A famous poem by Edwin Markham interprets the painting as representing the plight of the working man over thousands of year. I have provided a link to the poem for you, too. The poem is a form of artwork analysis in a way, sharing with the reader the ideas that the painting communicated to Markham when he saw it. The painting told him a story, and his poem is really about the ideas in the story. He discusses the details in the painting that make up this story, how the man appears, how he is standing, bent over, how tired he looks, and so on.
When you analyze a piece of art, think about the ideas it conveys to you. Then you must take note of what it is about the work of art that conveys these ideas to you. There might be symbols in the work. The setting might be important. The objects or people in the work could be important in telling the story and getting across the ideas. Your work of art might be a painting, a sculpture, or a photograph. Look at it carefully to see the story it tells and what it uses to tell that story. If you think about art analysis like literary analysis, you will see that the artist, like the author, uses various tools and techniques to get across the story and the ideas.