There are many ways to go about this, and it's important to think about the requirements. Are you supposed to write a structured essay, or just a paragraph? I will assume you are being asked to write a structured 5-paragraph essay. Here are my suggestions:
First, you might think about what the American Dream is to you. There are many perspectives about the American Dream, and many people look at it as a positive thing, while others look at it in more of a cynical way. Is this something you have discussed in class? When you decide what your idea of the American Dream is, you should discuss this in the first paragraph of your essay.
Your thesis should provide an overall statement of how Steinbeck addresses the American Dream in Of Mice and Men. Does he look at it in a positive light, or does he believe that the American Dream doesn't exist? Most people would say that Steinbeck believes the American Dream does not exist. An example thesis could be: "In the novel Of Mice and Men, Steinbeck shows that the American Dream does not exist because of the flaws of humanity."
Next, you want to include support for this statement. Your body paragraphs should outline reasons why you make the claim that you do, using supporting evidence from the novel. Each paragraph should have a topic sentence, and the rest of the paragraph should relate to that sentence. Ultimately, everything in the paper should relate back to your thesis statement.
Finally, you want to have a conclusion. The conclusion should sum up your ideas of the American Dream in general, and then briefly go back over the reasons that you outlined in your paper. The conclusion should not have any new information, and should clear up any confusion for the reader about your idea of the American Dream and how you believe Steinbeck addresses it.
Remember, it's not enough to just say what the American Dream is, but to discuss what you think Of Mice and Men says about the American Dream.