I will focus on one symbol, and then you can hopefully use that as a basis to think about other symbols in this text. You might like to think of the caged goldfinch as an important symbol in the novel. This caged goldfinch of course appears, when Henchard, feeling guilty about his behaviour towards Elizabeth-Jane because of her choice of husband, visits her on the day she gets married, carrying this bird as a gift. He puts it down in a corner while speaking with her and then leaves without it, forgetting it after being sent away by Elizabeth-Jane.
It is only a few days later that a maid in the house stumbles across the starved bird, which in turn causes Elizabeth-Jane to initiate the search for Henchard. Then of course she finds that he has died in the cottage of Abel Whittle. A parallel between the goldfinch and Henchard is explicitly established by Whittle when he tells Elizabeth-Jane about Henchard's manner of death, saying that he "didn’t gain strength, for you see, ma’am, he couldn’t eat," linking the goldfinch and Henchard's fate together. Not only did they both die of not eating and starvation, but we could also argue that there is another parallel between them, for both the goldfinch and Henchard lived and died in a prison. Whilst the goldfinch's prison was the literal cage, Henchard's prison was his own past deeds and personality, that entrapped him just as surely as the goldfinch was trapped.