It's unlikely that you will be able to co-author a paper as an undergraduate an English, for while we do participate in research, it's not the same as a lab where even the guy cleaning glasses can get his name in somewhere. I am a senior applying to graduate schools in English now and have gotten the opportunity to write 3 research papers at length (one which I'm not refining into my writing sample) and present at two undergraduate symposiums, so I can recommend some options.
If you have an area of research interest (even if it's something general like the post-modern novel), find a faculty member at your school who specializes in that interest and ask about individual study course options. If it's a professor you've had in class before, that's even better. Or, if your class professors don't specialize in that area, they can generally recommend someone who can and put a word in. Explain your intent to go to graduate school and that you would like to have some research experience.
See if your school does have some sort of undergraduate research conference in the spring/summer. If so, you have something concrete that you can discuss with a professor and a definite ending point for a research project if you begin to start one.
Otherwise, if you're a junior, start brainstorming ideas for your honors thesis. You will probably change your decision a million times, but it's good to start thinking. Since that's likely going to be your writing sample, the earlier you get started the more time you have to make it great. You're not going to be rejected from schools because you haven't published XYZ amount of papers or learned the so-and-so method; but you are going to need to prove that you have a grasp of major concepts in the field, are interested in and engaged in making contributions, and can write your butt off