Listen to a variety of Bob Dylan's music. By doing this, you will be able to get a feel for his singing style and how it has varied over time.
Consider listening to the works of some of the singers that inspired Bob Dylan's singing, including Woody Guthrie, Hank Williams and Leadbelly. This will help you pick up certain aspects of Bob Dylan's singing style and help you understand how Bob Dylan chose his recognizable singing manner.
Pay close attention to the music of Bob Dylan imitators to hear how they sing like him. Often, it is easier to imitate someone when you listen to the imitations done by others.
Read through Bob Dylan's song lyrics and get to know them well. His lyrics can often get very complicated, so it's essential to have the words memorized when trying to sing like Bob Dylan. Songbooks, such as The Definitive Bob Dylan Songbook, are available for purchase at bookstores or online.
Practice singing like Bob Dylan to instrumental versions of Bob Dylan's songs. This will help you get phrasing of lyrics in sync with the music, while helping you see how the lyrics and the music fit together.