There are a few good ways to come up with research paper ideas. One of the best ways is to research a topic, within the parameters of the assignment, that is genuinely interesting. Being interested in the research topic is a great way to make the processes of researching and writing much easier and more enjoyable. Before delving into a research paper, it is good to confirm the topic either with one's teacher or the teacher's assistant. Research paper ideas can come from topics that are discussed in class or in conference with one's professor or can come from one's reading that is conducted outside of the required coursework.
The first and often best resource is one's professor and the materials given out by the professor. Most courses are based on a few key topics and a few key points for investigation. Review the description of the course in the course offering catalog or as it is described on one's syllabus and see if there aren't any good clues for research paper ideas in those pieces of text. If those are not of help, visit the course professor during office hours to get some guidance and advice on research paper ideas.
Sometimes professors will even give out a list of topics that can be covered in research papers. This is a great resource and can often be used all semester long. If such a document does not exist, consider working with a campus librarian. A librarian will be able to review the research paper assignment and, at the very least, offer a list of papers, journals, books, and other reading materials that may yield research paper ideas.
Another good resource is the campus writing lab. Most campuses have such a facility where students can work with staff and graduate students who are skilled in coming up with research paper ideas. If all else fails, discuss research paper ideas with classmates. Be sure to get advice from students who are known to perform well in class and who might be able to offer good guidance on this point.