In high school English classes, teachers usually give students some help getting started. Generally, students already know what theme they are analyzing, or maybe they're choosing from a handful of potential themes. When you know your theme, it's not too hard to find a quote from the book that relates to that topic, but the next steps can be difficult. How do you use that quote to perform analysis? How do you use that quote to actually make a point?
The simplest and most reliable way to do it is with the CQC method: Claim, Quote, Connection. Different teachers will have different systems for how to organize your ideas, and that's fine. CQC is simply the logical structure that you use regardless of whatever sentence structure your teacher wants. Let's take a look at an example to make things more clear.
The Great Gatsby is a classic novel that most American high school students read, so we'll use that. One of those most prominent themes in Gatsby is "the American dream" and whether or not it is something that can truly be achieved. Now it's time to make a claim about that theme. As you might have learned in school, a claim is a statement that can be supported by evidence on either side. For this reason, "The American Dream is bad" or "The American dream is real" are weak claims. How could you provide evidence supporting either of these statements? They're too vague, and your evidence backing them up would be equally vague. One simple way to make a strong claim is to highlight cause and effect. For example, in Great Gatsby many of the characters pursue some kind of "American Dream," and many are unhappy. A simple connection between those two points would be the claim that "In The Great Gatsby, pursuing the American Dream leads to unhappiness." It's pretty basic, but good enough to make our point here.
Now that we have our claim, finding a quote should be fairly easy. As stated above, there are many unhappy characters in Great Gatsby, and many American Dreams. We might as well go with the title character. In Chapter 9, Nick watches Gatsby on the dock and thinks that "[Gatsby] had come a long way to this blue lawn, and his dream must have seemed so close that he could hardly fail to grasp it. [Gatsby] did not know that it was already behind him, somewhere back in that vast obscurity beyond the city, where the dark fields of the republic rolled on under the night."
This quote is much too long to use: teachers hate it when you quote huge blocks of text, so don't. The question is, which part of this quote suggests that pursuing the dream will make Gatsby unhappy? His dream seems close enough to grasp, but it's already behind him. Reaching ahead for something behind you seems like a problem, so that's our crucial point. Most teachers push their students to incorporate quotes into their essays, and there's a simple trick to doing it. Just use your own writing to introduce the context and cut the quote so that it starts with the part you want to focus on, like this:
Gatsby is reaching for the American dream, but "he did not know it was already behind him." (p.149) Bingo, now the quote is part of our essay!
Here comes the most important part: connecting back to our claim. If we cannot connect the quote back to our original claim, this has all been a waste of time. Luckily, we chose a simple cause and effect claim that is very much supported by evidence, so this should be easy. How does reaching and striving for something one has already accomplished lead to being unhappy? There are many ways to make this point, but the simplest arguments are often the best. We can say that if a person like Gatsby cannot appreciate the American Dream that he has achieved, then he will be left unsatisfied and unhappy. We've closed the loop: Our original claim was that pursuing the American Dream makes people unhappy, our quote provided evidence of a relationship between the American Dream and unhappiness, and our last sentence explained that connection clearly. Claim, Quote, Connection!
Remember, if your teacher has a specific structure that they want you to use for your literary analysis, you must follow their instructions. This CQC method is simply a tool for checking your work and making sure that you are following the key steps for performing literary analysis, no matter what the structure of your essay is.
Good luck, and write on!