There are many different types of market research you could conduct, which can make it confusing to know where to start. I frequently use this article as a reading assignment for homework, then students come to class to outline a plan for conducting research.
There are many different ways you conduct market research, such as surveys, focus groups, and product tests. This article details the different types. While this is geared at marketing in an established business, the techniques are still valuable to startups to see how it's done in successful companies.
This PowerPoint Presentation with instruction on what it means to conduct market research and a case study on how to apply the concepts. I don't use this resources to deliver the lecture myself but rather I assign this as reading homework for students.