Shepard graduated in 1965 from the segregated Garner Consolidated High School in Garner, as salutatorian of his class. After graduating, he received a four-year academic scholarship from Saint Augustine's College (now University) to pursue his undergraduate education. When he entered college at age 17, the civil rights movement was underway and bringing about changes to loosen the stranglehold the Jim Crow laws had on Blacks in the South. He received his B.S. in Chemistry in 1969, and married his college sweetheart Alzonia Wiggins that same year.

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After receiving his undergraduate degree, Shepard was awarded a National Aeronautic and Space Administration (NASA) fellowship from Howard Uiversity to pursue graduate studies toward a Doctorate degree. He started with the intent of obtaining the Ph.D. degree without first getting the M.S. degree. He changed his strategy when he and his major research advisor, Professor Jesse M. Nicholson met with researchers in the Mass Spectroscopy division at the Naval Research Laboratory (NRL) who saw great educational benefit ​in develop​ing a thesis at the M.S.-level through a collaboration with NRL before continuing for the Ph.D. In addition to his advisor Dr. Nicholson, Dr. Fred E. Salfeld, head of the mass spectroscopy research division at NRL, proved to be a factor in Shepard developing and following his research path, so much so that Dr. Salfeld was the external member on his dissertation committee.

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He conducted his research in the facilities at NRL, receiving his M.S. and his Ph.D. degrees from Howard University in 1971 and 1973, respectively in Physical Organic Chemistry with a focus in Mass Spectroscopy in collaboration with NRL.