The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper, we describe the design and validation of the survey, a process that included observations of students, a review of previous literature and textbooks and syllabi, faculty and student interviews, and statistical analysis. We also discuss issues in the development of specific questions, which may be useful both for instructors who wish to use the QMCS in their classes and for researchers who wish to conduct further research of student understanding of quantum mechanics. The QMCS has been most thoroughly tested in, and is most appropriate for assessment of (as a posttest only), sophomore-level modern physics courses. We also describe testing with students in junior quantum courses and graduate quantum courses, from which we conclude that the QMCS may be appropriate for assessing junior quantum courses, but is not appropriate for assessing graduate courses. One surprising result of our faculty interviews is a lack of faculty consensus on what topics should be taught in modern physics, which has made designing a test that is valued by a majority of physics faculty more difficult than expected. (Contains 9 figures and 5 tables.)