No permission is required to refer to copyrighted material, or to characterize the content of such material. The form of the citation you give, if any (APA, MLA etc) depends on the standards of your discipline. There is no legal requirement to attribute ideas to a source, or to mention what works James T. Kirk figures in. Course projects on such content can likewise discuss copyrighted materials with or without references / citations, depending on the rules of the instructor.
However, there are restrictions on copying such material. You are generally allowed to copy a bit of material, for educational purposes, under the "fair use" doctrine, which applies equally to students and instructors.
It is quite unclear what the limits are on classroom fair use. Typical classroom factors in favor of fair use are noncommercial, education use in class, the effect on market; on the opposing end are likely the amount of copying and the nature of the work (factual vs. creative). For instance, having students exactly re-create a sculpture is probably "complete copying", and a sculpture is the epitome of a creative work (thus, most protected). However, a fifth consideration is the "transformative" nature of the new work. In that case, students creating a new sculpture based on a protected work would be more transformative (adding new creative elements) than would be the case if the assignment is to make an exact copy.
The US Copyright Office maintains a fair use index which summarizes case law where fair use is relevant. In academic contexts, fair use is generally found, provided that you follow certain guidelines: get permission if a product is published, do not publicly perform a work without permission (a license), limit distribution of protected material to enrollees, obtain permission from the Copyright Clearing Center for text material, use sanctioned institutional distribution methods (e.g. closed course reserves, university licenses for articles and parts of books); do not avoid licensing fees (usually a consideration for the institute, not the instructor or student).