There are many strategies and tips for doing research, but generally, following these steps will work!
1. Make sure you're clear on the requirements of the assignment.
2. Use a calendar - mark the deadline and some deadlines for yourself in between! One good site!
3. Do some sleuthing - Credo, Wikipedia, Internet - just to get an idea of the background - looking for search terms.
4. Go deep! Find a few books on the topic. One example
5. Get some current information.
6. Think about what is important or what you'd like to know more about.
7. Organize your paper with an introduction, major points supported by details and a conclusion.
8. Write the paper - keeping tracked of where you're "borrowing" your information*
9. * List your sources
10. Proofread your paper.
For a detailed look at the process of writing a serious research paper, check out Georgia Tech's Research site.