Read the play. If you only read the summary or watch a film you're not really writing about Othello. The play isn't that long, especially when taken in pieces. Read one act a day until you're finished. If you have trouble understanding the language, find a text with good footnotes. The Bevington and Norton editions have excellent footnotes. Your local library should be able to supply you with a good edition.
Do historical research. Read a little bit about what it was like to be a Moor in 16th century Venice. Information about race relations in 16th century Europe and The Crusades will be invaluable when thinking through the plot and characterization in the play. Since the plot is partially driven by these concerns you will need some information to understand the text.
Do critical research. There are academic writers who have already written about this play. Reading some of their work can help you to formulate your own ideas and can help eliminate ideas that are less helpful for your paper. Look up one or two critical articles in a respected Shakespearean journal such as Shakespeare Quarterly. They may have some difficult language, but they can give you an idea of what others have written about this play.
Write. Take the information you've learned from your historical and critical research and put it together with your own opinions. The paper shouldn't be about the research you've done, but you should use it to inform your own thoughts. For example, writing in your paper that Othello was mistreated because Iago didn't like him may be true, but you'll need to acknowledge the historical mistreatment of Moors at the hands of Europeans for your analysis to be complete.
Edit. Run the spell and or grammar check in your word processing software and fix any errors. Read your paper out loud and listen for mistakes. Send it to a friend or teacher for review. Print out the paper and cut the paragraphs out, then rearrange them in the way that makes the most sense to you. Read it out loud again and fix any remaining errors. Perform these editing steps for any paper you write.
Turn your paper in on time. You might write the best paper possible and still lose points if you hand it in late.