Part of the task of choosing a research topic has already been decided by virtue of the subject of the class. Read the syllabus carefully to ensure you understand what the teacher is looking for in the assignment. Write down any questions you have and approach the teacher with them during the posted office hours. Most teachers are glad to discuss assignments, as it shows an indication of the amount of effort the student is willing to make.
The coursework already covered provides the parameters within which to select a topic. For example, there are a limited number of writers who could be an appropriate subject for a research paper in a class on writers of the Beat Generation. Unless the teacher has stated otherwise, the pool of available subjects will be limited even further to only those works which have been discussed in class.
So you've chosen a subject to cover, now how to narrow that down even further into an interesting research topic? Here's where brainstorming strategies come in handy. One useful technique is called freewriting. As explained by Janet Burroway, simply take out a clean sheet of paper and start writing down whatever thoughts pop up. Try to steer your thoughts toward the research paper subject and write down whatever comes up, even if it doesn't seem to make a lot of sense. The idea is to let the subconscious mind take over and throw out some ideas that the conscious mind might be blocking.
Another technique described by Burroway is called clustering. Write the subject on a sheet of paper and circle it. Then free-associate related words around the initial subject, connecting them with a line and circling them so that they can become new subjects to free-associate from. This technique is similar in concept to word association party games. The goal is to fill a sheet of paper with subjects that can be connected to form a topic. Choosing a research topic is essentially about finding a perspective to write from, and free association exercises can help a writer find the connections with which to create a context for perspective.
If you've got some ideas but you're still not sure how to express them as a topic, start by phrasing the ideas as a question. For example, a cluster of ideas involving Allen Ginsburg, his poem "Howl," and his influence on the counterculture, could be phrased as, "What role did Allen Ginsburg's "Howl" play in inspiring countercultural thought?" Answering such a question is the purpose of a research paper, and the distilled answer to the question becomes the topic statement.