There are lots of good ways to write a paper. Not every method will work for every student, so if anything in this list doesn't feel right to you, feel free to follow your own method. What you see here is a general outline of the steps I take when I write a paper.
1. Don't procrastinate about this project. People who write things at the last minute almost never do their best work. In fact, research shows that when you give yourself lots of time to think about something you need to write, your brain is concentrating on the problem even when you are not. Think about the paper several times over several days. The process I've outlined below should take a few hours, but if you spread your work over a week or more, the process is less arduous and you give yourself the best chance of being successful.
2. First, choose a topic. Your topic should match readings that interest you at least a little. Don't compare Locke and Hobbes, or Jefferson and Hobbes, if you don't like their work. Don't analyze Candide if you don't like Voltaire. (Yes, there are some students who hate everything we study, but please bear with me-I don't write this stuff, I just teach about it.)
3. Gather evidence. After you choose a topic, it's a good idea to simply list the ideas, or events, or quotations from each work that correspond to your topic. If you want to say that Locke influenced Jefferson, you need to find instances in each work that sound similar. If you think Voltaire probably was a deist (deism: "a movement or system of thought advocating natural religion, emphasizing morality, and in the 18th century denying the interference of the Creator with the laws of the universe), then you need to find examples of "natural religion" or instances where the novel shows that Voltaire thinks God does not interfere with the affairs of humans.
4. Create several claims. Once you have gathered the evidence, you will usually find that it breaks down into several types. People who write better papers usually break the topic they choose into three or more pieces, showing how several pieces of evidence relate to a particular aspect of the topic. For example, Essay Two, Topic Five asks you to relate several courtship rituals together to show how they exemplify some cultural conflicts. You might show how some show conflicts between genders, others conflicts between social classes, others conflicts between different cultures. To answer the Locke/Jefferson question, you'd want to show places where Jefferson borrows from Locke, others where he changes or reinterprets Locke for a his own situation, and others where Jefferson may borrow from somewhere else or present his own ideas.
5. Write the body paragraphs. Some writers like to begin with their introduction, then follow the outline contained in the intro. On the other hand, others (like me) don't really know what the center of their paper will be until they write it. If you need to "work out the details" before you decide how to introduce and conclude, the next step is to write each paragraph separately, then put them together. If you are typical, you make the claim in your first sentence, then present your evidence in the rest of the paragraph, with a summarizing sentence or two at the end. Remember that properly cited quotations that are appropriate and that you explain after you present the quotation tend to make your writing more impressive.
6. Create transitions. Better papers also move smoothly from one idea (and paragraph) to the next. To do this, either the last sentence of one paragraph or the first sentence of the next has to show some connection between the ideas contained in each paragraph. Transitions aren't as important as well-stated claims that you back up with evidence and a consistent focus, but they can make your grade higher, since they show grace in your writing and help the reader keep a focus on what you want to say.
7. Write your introduction and conclusion. Now you are ready to give me a summary of your major points with a specific statement of the overall goal of your paper. Please don't say "My overall goal is . . ." however. Instead, make a simple statement, being as specific as possible about what we will see later in the paper. Academic papers are expected to state their "opinions" (arguments, theses) as facts, and are not supposed to refer to themselves.
BAD: "This paper will show you how Odysseus demonstrates his strong body and intellect"
BAD: "I think Odysseus shows his strength and cleverness several times during The Odyssey."
GOOD: "Odysseus demonstrates his strong body and intellect
in his meetings with the cyclops, the sirens, and after he leaves
the island of Calypso."
Your conclusion should be different from your introduction but should also have some similar elements. It should restate your thesis (though not in exactly the same words), but then it should do something with that thesis: show how the topic relates to the modern world; draw some new implication from what you have discovered; explain what knowing about the topic has done for your own thinking about life.
8. Proofread and edit. This step you should do three times yourself. The first two times, make sure everything makes sense and that your ideas flow naturally one to the next. Also pick out any mechanical problems. The third run through, read the paper backwards. That's right, read the last sentence, then the next to the last, then the one before that, and so on. Since most writers are very used to seeing their own writing, it is sometimes hard to edit your own work, especially after you have been writing it and reading it for awhile. Reading the paper backwards breaks up your familiarity with it.
Finally, give your paper to someone else you trust. Find someone in your circle who writes good papers, and ask them to look it over. While you don't want to give your paper to someone who will hack it to death and depress you, you also shouldn't share it with someone who either doesn't have the time to really read your paper, or to a friend who doesn't want to hurt your feelings. When I have something really important to send out (and papers for classes were always important to me), I got another English major to look it over.
9. Finish it on time.
10. Turn it in on time.