Are you referring to literature? If so, there are several ways to figure out symbolism.
- Does the same object seem to occur often in the work (such as the scarlet letter A in The Scarlet Letter.) If so, then this object is significant. It has meaning in the novel, usually related to the theme. The "A" stood for "Adulteress" but what else could it mean? In Moby Dick, the white whale pervades the entire action of the book. What could this symbolize? Why was Moby Dick white? What does this color symbolize?
- Does the author spend a lot of time writing about a certain object, event or person? If so, it is probably important. It may be symbolic of something else. The raft that Huck Finn and Jim float on is described in great detail. What happens to Huck and Jim while they are on the raft? How does this differ from what happens to them on land? The raft is a symbol of something else.
- What is the writer's style like? Does the writer focus on certain themes over and over, like darkness or prejudice or conflict? If so, what are some objects, characters or motifs that keep appearing in the work that might symbolize this? In Heart of Darkness, there are a lot of dark colors, dark imagery. What does this symbolize? What is dark? Life?
- It's OK to do research. If you are reading a novel and have to write about symbolism, see what other scholars have to say about the symbolism in the work. Just make sure you use citations when the ideas are not your own.
Many of my senior literature students would get angry at me for even suggesting we discuss symbolism in literature. They claimed I ruined the reading experience for them. There is a school of thought that supports this, but my view is that the discusison of symbolism enriches the reading experience. Reading The Chronicles of Narnia as a child was a very different experience for me than reading it as an adult, with an understanding of the symbolism and allegory. The tales took on a much deeper meaning, and the experience was much more profound.
Consider this: during a discussion of what Christ's cross symbolized, one of my students said, "It symbolizes death." Another student raised his hand and offered, "I disagree. To me, it symbolizes life." So there you have it.
See this link below for a funny story about Harper Lee and what she had to say about symbolism in her novel. This is not a scholarly website and I don't know if it is true, but it is germane to this discussion.