How should I go about an essay on the topic "Choose a character you identify with from either The Hunger Games or Catching Fire and explain how you relate to the character"?

It is hard for me to get too specific on this topic since I do not know which character you identify with, but I can give you some general advice. First, to choose a character you identify with, you need to identify a character that means something to you personally. This could be someone that seems to be like you, or someone you admire. For example, you might admire Katniss’s frankness and courage. You might admire Peeta’s loyalty and skill. Either way, the choice of a character is the first step.
The second step is to find a series of reasons why you identify with this character. It is an essay, so you should list three reasons why you identify with whichever character you choose. For each reason, you need to choose a supporting quote and then explain how the quote is relevant to your point.
Let’s say you choose Katniss as the character you admire because she is brave, loyal and intelligent. One of the examples you could give is her famous act of choosing to volunteer as tribute in her sister’s place for the Hunger Games.

I don’t need to shove through the crowd. The other kids make way immediately allowing me a straight path to the stage. I reach her just as she is about to mount the steps. With one sweep of my arm, I push her behind me.
“I volunteer!” I gasp. “I volunteer as tribute!” (Ch. 2)

This quote could be used to describe Katniss’s commitment to her family, her bravery, or her strength of character. You could explain how she is selfless and refused to allow her sister to go into the Hunger Games, choosing to risk her own life instead.