First and most obviously, you have the mockingjay itself, which is a symbol of the revolution. It is an interesting one, because the mockingjay is a creature born unintentionally as a result of the Capital's meddling in the affairs of nature and human lives. It is an unintended consequence of their rule, just as the rebellion is an unintended consequence of their harsh rule for so long. Katniss herself becomes another symbol of the mockingjay, or a visual cue that symbolizes the entire emotion and drive of the rebellion itself; she beomes the living symbol, whereas the mockingjay is the token of the rebellion.
Fire too becomes a symbol; in the previous books, fire was often used in the imagery surrounding Katniss and Peeta, due to their district burning coal for its living. That fire comes to represent the rebellion also, in both positive and negative ways. Fire is associated with Katniss and her symbology for the rebellion. However, as District 12 is torched and burned to the ground, fire also becomes a symbol for the destrution that occurs in war.
Another symbol used in the novel is that of the rose. President Snow is fond of roses, and his visit to Katniss in Catching Fire forever implants an association between Snow and the rose in our minds, along with Katniss's. President Snow tries to use that to his advantage by leaving her gifts of roses along the way, and using the scent of the rose to sicken and weaken her. The rose is a symbol of President Snow's power and corruption, and of how the Capital is full of beauty on the surface, but is sickening at its core.
Those are just a few symbols that are evident in the novel; I hope that helps to get you started. Good luck!