Schuster was born in Brooklyn, New York in 1935 and raised in Far Rockaway. He attended Columbia University as an undergraduate and received his bachelors degree in chemistry in 1956. He then moved to the California Institute of Technology, from which he received his Ph.D. in 1961 under the mentorship of John D. Roberts. During Schusters time in the Roberts laboratory, the group began experimenting with some of the first applications of NMR spectroscopy to organic chemistry. Schuster next joined Howard Zimmerman's group at the University of Wisconsin as a postdoctoral fellow, where he spent a year studying mechanistic organic photochemistry.