Fisk was the last direct pupil of Andrés Segovia and is the holder of all reproduction rights to Segovia's music, given to him by Segovia's wife, Emilia. After attending Jamesville-Dewitt High School in Dewitt, New York, Class of 1972, Fisk also studied interpretation under harpsichordists Ralph Kirkpatrick and Albert Fuller at Yale University, where he graduated summa cum laude in 1976. After graduation, he was asked to form the Guitar Department at the Yale School of Music. He was the winner of the International Guitar Competition in 1980.
He is a professor at the Universität Mozarteum Salzburg in Austria, where he teaches in five different languages, and in Boston at the New England Conservatory. His students have come from many countries, and several have gone on to become important performers and teachers in their own right.
Fisk lives in Boston, Salzburg, and Granada, Spain with his wife, Zaira, and their 6-year-old daughter, Raquel. He uses a handmade Thomas Humphrey Millennium guitar and another by upcoming luthier Stephan Connor. He received the Grand Cross of Isabel la Cátolica on June 10, 2006, from King Juan Carlos of Spain. Earlier recipients have included Andrés Segovia and Yehudi Menuhin. Fisk earned the award for contributions to Spanish music as an interpreter and teacher.