Publication a prerequisite for PhD Programs
Publication is not a prerequisite for PhD programs. To be specific, the only requirements for a PhD program are those published by the particular university department in the official degree catalog.

But having your name on some published articles before applying for PhD programs, and including your publications as part of your "pitch," sure makes for a more competitive application.

To get started doing research, talk to your advisor, faculty members whose research areas are similar to yours, look at research assistant positions (anywhere, not just at your school), and so on. Most importantly, define some questions that you want to research, dig into the literature, and just get started on your own. Then let your rough investigation be a conversation starter with local and other faculty.