It may be helpful to begin with this quick overview: How to Write Research Proposals for Political Science.
Once you have chosen a political science research topic, you will need to do a literature review to see what else has been written on this subject. Use the links in this guide to help you search for scholarly articles in periodical literature and other academic writing in books, theses, and dissertations.
The JEWL search option allows you to search through hundreds of specialized and general interest databases. If the results list is too overwhelming, then start with the smaller Academic Search Ultimate database.
This video from North Carolina State University explains the basics of conducting an academic literature review.