Read the piece of literature at least once in order to formulate an argument on it.
Read literary criticism on the piece of literature in order to get an idea of insights that you may not have had on your own. This is not to say that you should plagiarize, but other writers will often approach literature from an angle you hadn't thought of.
Create your thesis, or argument. This should be a point that has to be defended rather than something that is inherently obvious. So, it should not be directly related to the plot ("Romeo and Juliet are lovers in the play of the same name") or about the genre (" 'Romeo and Juliet' is a romantic tragedy by Shakespeare"). "Romeo's love for Juliet is his projected homosexual love for Mercutio," however, is definitely debatable and will need to be packed up in your essay.
Write some rough notes, using the piece of literature, to back up your argument. Make sure you write down page numbers when you find examples. They can be maddening to look up again later.
Write a rough outline of your essay. Each paragraph should open with a sentence that directly responds to the thesis; this is a good place for you to ensure that you do this. This is also a good place to make sure your argument flows logically. There are a number of ways to do this; you could proceed chronologically through the piece, citing examples as you go through and explaining how they back up your thesis, or you could approach from the angle of different characters, or essentially anything else as long as it is logical. It is not wise, however, to start chronologically then move into a character-based argument, or vice-versa. This mixing and matching looks disjointed and makes it difficult to read and follow.
Type a rough draft, using your outline as a guide.
Edit the rough draft for grammar, style and flow. Someone unfamiliar with the piece and with your essay should be able to read it and understand the key points of your argument.
Rewrite as needed, then repeat step 7 as many times as you deem necessary. Once you're content, print it and hand it in.