How do I co-author my first paper?
You don't first co-author a paper, you first collaborate on a research effort. Then, if said research effort leads to interesting results, you co-author a paper. So you need to look for someone doing interesting research that you think you can contribute to. Talk to professors in your department and ask about the research they and their students are doing.

Of course, since co-authoring a paper is important to you, when you find the opportunity to be part of a research project you should ask the professor: "Do you think this is likely to lead to a paper before I graduate?" Nobody can promise you a paper (even if you do everything right, the nature of research is that we don't know everything in advance). But he/she will probably have some intuition about it. You should also ask what you specifically need to do to merit co-authorship credit on the paper that comes out of the research.