In order to find a mentor you will need to decide what research area interests you. You may want to discuss this with your academic advisor, a professor, or a TA in one of your courses. Often they can give you ideas about faculty who are working within your area of interest. However, there are several ways you can learn of potential mentors on your own. All involve identifying a faculty member on the basis of their area of research and reading about their research before approaching them.
Visit the web pages of departments on campus. Many departmental web pages have links to web pages of individual faculty members where descriptions of their research can be found. Use a searchable database to search for a topic that interests you. One such database is the Community of Science.
Read about the research of potential mentors. The faculty web pages you visit probably have a brief overview of the research projects going on in their laboratories and research programs. In addition, many faculty web pages list some of the publications that the faculty members have authored. You may want to locate some of these publications at a campus library and read them for a more in-depth background before approaching the potential mentors. You may find that these publications are written at a level that is hard to understand, given your exposure to specific scientific areas thus far, but you will be able to get a basic idea of what the research involves by reading the Abstract and Introduction portions of the research article.