The first thing that most students learn in graduate school is that taking classes is fun, and teaching is rewarding, but research is hard and sometimes frustrating. Therefore, there is a tendency to focus on the first two legs, and put off either the initiation or the completion of the third. This is a mistake; all graduate students should be involved in research from the first month of their graduate careers. If you do not yet have a clear idea for a research project, ask your advisor -- they will help you find a project. As you progress through the program, you will become increasingly independent of your advisor. However, science is necessarily a collaborative enterprise, and it is the rare (and not necessarily the most successful) student whose dissertation is entirely independent of other work going on in her/his/their advisor’s laboratory. Most of your research will be conducted in collaboration with your advisor, but it is a good idea to do some research with someone else in the program. It broadens you intellectually.
The Department requires a second-year research project of all students, but you should be involved in research at some level during your first year as well – not least because it takes more than one year to get a research project off the ground and see it through to fruition. The purpose of the requirement is to ensure that students are involved in research throughout their careers as graduate students. Accordingly, the second-year project should reflect work done at Berkeley since the time of your matriculation in the doctoral program.
Note that it often takes two years to complete even the simplest study. Accordingly, do not put the initiation of your second-year project off until the end of the first semester of your second year. You should have a clear idea of what you are going to do before the end of your first year, so you can complete data collection, analyze your data, and write the project up before the end of your second year. It may seem silly to say so, but do not plan on a five-year longitudinal follow-up study for your second-year project.