One very important theme in The Hunger Games is the importance of personal freedom vs. government control. All the citizens of Panem are oppressed and directly controlled by the government through force; because they are deliberately kept poor and starving, the Districts cannot rebel. Katniss, the protagonist, is a very independent and individualistic girl, and defies the Capitol as much as she can, hunting illegally to keep her family fed. When she is placed into the Hunger Games, she acts out of self-preservation, but then manages to change the rules of the game, threatening the Capitol's control. By publicly showing the power of personal choice, Katniss is able to spur a real rebellion against the Capitol.
Theme, as I understand it, is basically a one or two word description of the moral of a story. In other words, “What am I supposed to learn from this?” There can be many themes in one story. For example, love is a common theme, and so is unrequited love (that is love where one person feels something for another, but it is not returned). In Collins’ The Hunger Games, it is evident that love between sisters, and the unrequited love between Peeta and Katniss both exist as a tool to make the novel more interesting and to make the reader feel something for the characters when something good or bad happens to them.
In short, the theme exists as a backdrop for what happens in a story and serves as a message or moral. Some other themes in this book are survival, man vs. nature, man vs. man, and man vs. self.
I would say a good theme for The Hunger Games is always put family first.
There are several themes developed throughout the story. To identify a theme, one must identify repeated ideas. For example, throughout the story, the author uses elements of the setting, thoughts and actions of various characters, and events in the plot to demonstrate the extent to which the government controls the citizens of Panem. Make a list of these examples (i.e. District 12 is enclosed by a fence, necessary survival resources are withheld, youth are forced to enter the reaping). Once you have a list of examples, you must decide what the author is trying to communicate to the reader about the recurring idea, in this case excessive government control. This recurring message presented throughout the story constitutes a theme. Some other repeated ideas you might develop into themes are "survival", "reactions to grief/anger/distrust", and "humanity vs. inhumanity".
Killing people is never acceptable.