My courses frequently require engagement with assigned sources. Let me explain what that means in more depth than the syllabus allows.
The purpose is to evaluate students' comprehension with the texts and other media assigned in the course syllabus. Think of it as an open-book quiz. I do this so that more artificial evaluations like exams are not necessary. But in order for this purpose to be achieved, I want to see that you can do the following:
Summarize a central idea of the source with accuracy and precision—and in your own words, with or without quotations.
Apply that idea to the analysis of something external to the source, such as your own research topic.
Approach the idea critically, with a well informed analysis of its insights and shortcomings.
Take your time with this. Dwell with the source as long as necessary to accomplish these goals.
A few pitfalls to avoid:
Using the source in a way that is superfluous or superficial. If it is tacked on, readers will know it. Make sure the engagement contributes something useful to the project in which it appears.
Relying too heavily on quotations. If all you do is quote the source, I will not know that you actually understand it. Choice quotes are great, but what you say in your own words matters much more.
Interpreting part of the source out of context. If a writer outlines an idea in order to argue against it, do not act as if that idea is the writer's own point. Make sure to interpret any part of the source in light of the whole.