Throughout his teens, Nelson was singing and studying voice at every opportunity, imitating recordings of great baritones; Ruffo, Scotti, Amato, Campanari, and Werrenrath. He followed the track of many young singers, doing free and low-paying recitals for women's groups and in the then-popular society theatricals.

His first professional break came in 1922 when he was singled out by the press for an appearance in a society theatrical, The Marriage Tax. He also performed in Gilbert & Sullivan operettas with the Savoy Company at the Broad Street Theatre.

Alexander Smallens, musical director of the Philadelphia Civic Opera and later assistant conductor of the Philadelphia Orchestra, became interested in Nelson's career and gave him "serious coaching." In a 1936 career profile put out by Arthur Judson Concert Management, Smallens is credited with Nelson's "operatic success."

In 1924, Nelson won top prize in a competition which included a chance to appear with the Philadelphia Opera Society. He studied briefly with the noted teacher David Scull Bispham, a former Metropolitan Opera singer, but when Bispham died suddenly, Eddy became a student of William Vilonat and, later, Edouard Lippé. Lippé became his principal teacher for many years, even appearing in a small role in his 1935 film, Naughty Marietta. In 1927, Eddy studied opera in Germany, but turned down a chance to sing with an opera company in Dresden because he was homesick.

Back home, he began a concert career in 1928, accompanied by a young pianist named Theodore (Ted) Paxson. Paxson remained a lifelong friend and was on stage accompanying Eddy 39 years later on the day he died.

In his later years, Eddy frequently changed teachers, constantly trying new vocal techniques. He also had a home recording studio where he studied his performance. It was his fascination with technology that inspired him to record 3-part harmonies (soprano, tenor, baritone) for Disney's "The Whale that Sang at the Met" sequence in Make Mine Music.