You should seek to participate in undergraduate research if you are interested in a graduate degree.
The PhD is a research degree. As a PhD student you will spend several years conducting research, which will be written up in papers and also presented at conferences. Hence, one important thing that PhD admissions committees look for in applicants is prior research experience. The more deep and lengthy the research (experience), the better. Consider working in the summers (it can be a paid position) or taking independent research during the school year for course credit. Your research experience can start as early as your freshman year; the earlier the better. If your institution does not offer research experiences for undergraduates (REU), apply for REU’s at other schools. Internships at national labs or at companies can also be a valuable way to get research experience. The strongest applicants will have made presentations about their research at national conferences, or have even published a journal article. (Publishing a paper, although not necessary, is a fantastic accomplishment that can make your application stand out.) Another benefit of conducting research as an undergrad is that your research mentor(s) can be asked to write letters of recommendation for your applications. These letters carry significant weight because they will presumably comment on your research accomplishments. Finally, an undergraduate research experience is the best way to decide if you actually enjoy research. The open-ended, independent aspects of research do not appeal to everyone. It is important that you are convinced that you enjoy the research process before committing to the time needed to complete a dissertation and earn a PhD.
Other examples of research experiences
There are a lot of opportunities to participate in undergraduate research. One of the most straightforward ways is to find a professor you want to work with your university, preferably someone you’ve taken a course with, and tell them you enjoy the topics in the course and would love the opportunity to do research with them. Approaching your professors in this way may seem daunting. It may be difficult to put yourself out there. However, professors, on average, will be very glad you asked (especially if you are engaged in their course). They became professors because they find the process of teaching and training students, like yourself, enjoyable.
You can also look to see if your school offers an honors program for your degree. If so, you can apply to the honors program. Most honors programs require that you write an honors thesis on a research project you conducted. Thus, if you are accepted into the honors program, you’ll have a research project built into your degree. (You may still have to search for a professor to work with you.)
More research opportunities can be found by talking to older students and administrators at your school or from a Google search of some of the keywords here and the name of your university (or other universities you’re interested in). At most research universities, there are dedicated programs for undergraduate research.