Your research will always start with a question or assignment from your faculty member. How specific this request depends on a number of variables, such as personality, mood, weather, etc. It's always a good idea to write down as many specifics about the request as possible, and don't be afraid to ask questions to get the answers that you need. More often than not, your faculty member has a specific goal in mind, and you may need to ask questions to properly understand that goal.
At the Law Library, we've developed a research worksheet that you can use to help organize the information you've been given and develop a plan for your research. Feel free to make copies and use it as you're given research assignments.