Map out a tentative research plan. Doing so will give you direction and will likely spark more deliberate thinking about where to search.
Use a research guide, those available on the Chastek Library website and elsewhere online. Subject-based research guides have already pulled together key material on their topics. Consulting them can efficiently point you to the best sources. Oftentimes there will not be a research guide on the specific topic of your paper but there may be a research guide on the larger topic within which your paper falls. Guides can be found through general internet searches.
Ask for assistance early and often at the Reference Desk.. Librarians can suggest a strategy if you don't know where to start. Advise you on hard-to-locate and hard-to-cite sources, confirm that you have exhausted all possible Library and publicly available resources.
Don’t get caught in Westlaw and Lexis rut. While these are both deep and well-functioning legal databases, it goes without saying that many many topics will need material from and citations to materials not available on those databases including monographs, data, inter-disciplinary articles, historical sources, and so on. Also, simply stepping out of the Westlaw and Lexis box may spark crucial new ideas and directions.