You need to think too on how and why a character changes and develops during the course of this play. In this tragedy characters respond to situations and happenings that show us new sides or elements of their character, and these are important to think about and discuss in your essay on character. This is an important element to consider along with motivation (what does a character want and why) and actions (how do they try to achieve their aims).
I have my Honors 9th grade students examine Iago's motives in Othello. As this is the first research paper many of them have written, I provide them with three articles of cricitism (all can be found on enotes) that suggest different reasons for his behavior. (One says race is the driving force behind his plan, one says he's jealous of other characters' relationships, and one says that his ego is what causes him to act the way he does.) Essentially, the thesis statement usually comes out looking something like this:
Though readers will never know for sure why Iago acts the way he does, literary critics have offered different explanations for his behavior.
It appears that you have been asked to write a character analysis by researching a character from the play. There is a plethora of literary criticisms on various websites including NetTrekker, enotes, etc. An interesting slant to writing this paper might be a psychoanalytic study of a particular character and the various motivations for their actions in the play. Case in point would be Othello; look up information on the Moors of that time period and examine the effects of being an "outsider" in the world of Othello during the time period. Psychoanalyze how Othello's race could have affected his self-esteem, the constant second guessing of his actions and the need to confide in Iago. Looking at the other answers provided for structure and content, you are well on your way to writing a very interesting research paper or character analysis. Get your topic approved by your instructor before doing this to clarify that this is what he/she is looking for.
You say "research paper", and if I understand correctly, that is slightly different from a character analysis. You might want to check with your instructor before you start writing. If you are required to do research that does not begin and end with the text (Othello), then what you have to do is to read what some of the literary critics have to say and position your reading against theirs.
This would be an unusual request as most instructors discourage their first year students from looking for outside information, so please ask your instructor to clarify. If you are required to to a research paper using outside sources, go to your college library (or the closest university library), find some critical readings of characters in Othello. There are also some critical commentaries on enotes (see below).
Choose one character to write about. Your instructor will either want you to summarize critical comments or will want you to position your argument against these other interpretations of the character (again, check). It is important that you are accurate when you write about what others have said, and that you are clear in separating your ideas from others.
Typically, you will accept most of what others have said, but will find one small point/ interpretation that has not been fully considered by the critics. If you are expected to have your own interpretation, this small point of departure from the others will be your thesis.
Bdmadnick's answer is very good, I just wanted to add a cautionary note. It is easy to get bogged down in plot when you are writing about character. A sentence or so is typically enough to remind your reader of the event(s) you are discussing. If you wonder whether you are beginning to get off topic, ask yourself "how does this detail reflect what I am trying to say about the character? How does it enhance or develop my thesis?"
If you can't satisfactorily answer these questions, it is more than likely that your audience will wonder what your point is as well. Continually ask yourself these questions as you write to keep your focus.
When you write about a character, you need to explore the characteristics of that character. Sometimes the physical aspects are as important as the mentality of the character. In the body of your paper, state Othello's characteristic, and then explain it, using specific examples from the play. Direct quotes are also useful to show what a character is like. Othello is manipulated by Iago to distrust his wife, Desdemona. His jealousy of her leads to her murder by Othello.
Also important is how others view Othello and how Othello views himself. He believes he's a man of the world through his military experience. He's confident in himself, but his decline from a hero to a savage murderer leads to his self-destruction. He thinks he knows Iago, but Iago knows how to push Othello's buttons to get him to do what Iago wants. Iago's manipulation of Othello is like a puppeteer pulling the strings of his puppet. Iago uses Othello's weaknesses to bring about his downfall. Iago knows Othello feels alientated in a sense by society because he's an outsider.
If you go to the enotes link below, you'll find a great deal of information to help you with your paper. Good luck!