Diction is a term we use to describe an author's word choices. Individual word choices are never arbitrary because every single word carries its own connotation. Hence, an author's choice of one word over another will influence the tone, mood, and even meaning of a work of literature. Dr. Wheeler gives us the example of a "rock formation." A rock formation can be called "a stone, a boulder, an outcropping, a pile of rocks, a cairn, a mound, or even an 'anomalous geological feature,'" and each term choice for rock carries its own meaning (Dr. Wheeler, Literary Terms and Definitions: D"). For example, the term "anomalous geological feature" might be reserved strictly for scientific reading and carry a scholarly tone, while other word choices for rock in literature would convey different images. In particular, a boulder is understood to be much larger than just a stone, so a boulder might convey a harsher, more frightening mood than just the word stone. Similarly, both cairn and mound are understood to refer to a "heap of stones," but cairn is less frequently heard than mound and can convey a more intellectual tone than mound. So, to analyze diction choices in Catching Fire, all one has to do is begin zeroing in on individual word choices and thinking about the word's connotation. Below is an example to help get you started.
Just looking at the very first page, we see many interesting word choices, particularly the word flask used in Katniss's opening description: "I clasp the flask between my hands even though the warmth from the tea has long since leached into the frozen air" (p. 1). A flask is understood to be a metal or glass bottle used to carry liquids, but what's particularly interesting about the word choice flask is that it's first listed definition identifies a flask as especially being used in laboratories for science experiments (Random House Dictionary). However, instead of being in a laboratory, Katniss is in District 12 outside in the freezing pre-dawn morning as she illegally checks her hunting trap lines in the woods, dreading the moment when reporters and camera crews arrive to mark the moment that she and Peeta begin their victory tour. Since she is out in the woods, a more traditional word choice to describe the vessel she is carrying her now cold tea in would be canteen, which is a container to carry liquids especially used by "soldiers and hikers" (Random House Dictionary). The word choice flask rather than canteen provides an image that helps capture the dictatorial government that Katniss is under. Just like rats in a laboratory, everything Katniss and her people do, such as playing the Hunger Games, is done at the government's bidding so that the government can prove its superiority. Katniss and her people are socially trapped, just like lab rats. In contrast, the author would have created a much more wholesome image, like camping, had she used the word canteen.
Diction as a term refers to word choice. As my English teacher taught me, you can't just say "the author uses diction" in an essay. The word diction by itself only means that the author chose words to string together. You need to describe "diction" with an adjective - negative, positive, harsh, accusatory, comforting, etc. These adjectives in turn describe the effect of the ______ diction on the reader. Negative, harsh, or accusatory diction in a persuasive essay may cause the reader to feel more strongly against a certain idea. Positive and comforting diction in a story may calm readers and make them feel happy.
Diction and its effects can be determined by zeroing in on specific terms or by taking certain passages as a whole. Without going into specifics (I see that the previous answer has given several in case you'd like some), I think you'll find that the parts of the novel when Katniss is discussing the Capitol or President Snow will be filled with negative diction. This causes readers to in turn dislike the Capitol and President Snow because the words presented to us describe them in such despicable terms. This feeling is because of the ideas we have linked to the words themselves.
tl;dr - diction is word choice and it affects readers because of the feelings readers get from the words. Knowing that, it should be easy to locate specific uses of diction in passages of Catching Fire - descriptive passages in particular should show obvious diction.
Peeta says that Katniss was pregnant it suprises readers that he would say that