In this paper, we present an introductory course design for fresh research-based graduate students in wireless communications, which is planned to be delivered immediately after enrollment. The course aims at covering necessary research methodologies and the rudiments of wireless communications. Different from most graduate study curricula based on experiments, we design the course structure in an introductory manner by tailoring the course contents to a simplistic form and involving only simulations. We start by introducing the pedagogical background and our motivations for designing this course. Then, we present the fundamentals and the technological contents, followed by detailing the basic research methodology, strategies, and skills for deriving insightful analytical expressions and carrying out numerical simulations. We also verify the effectiveness of the course structure design by carrying out a teaching experiment and analyzing objective and subjective data collected from the experiment. By participating in this course, research-based graduate students are expected to gain preliminary knowledge of the research methodology and strategies in the field of wireless communications as well as a research roadmap.