While it may seem obvious, having at least some musical training is important. Even if you're not a performer, you must be able to market your songs. Stephan Citron, author of "Songwriting: the Complete Guide to the Craft," lists Billy Joel, Barry Manilow and Joni Mitchell as songwriters who compose, write their own lyrics and do their own orchestrations.
Every successful songwriter finds a target audience and is able to hold that audience. Some examples include Bob Dylan and Joan Baez addressing the counterculture of the 1960s, or Curtis Mayfield singing for politically disenfranchised African Americans in the 1970s.
All songwriters go through a period of rejection before establishing their careers, and many even experience creative lulls well into their careers. Songwriters must be able to reinvent themselves if necessary.
Successful songwriters know their own voices and avoid emulation. Why settle for an imitation when the real thing is available? Even if the listener can detect various influences, successful songwriters sound only like themselves.
Since many songwriters are not proficient at both composing and lyric writing, the ability to collaborate is important. Many great songwriters are attached to specific collaborators, either as lyricists or as musical arrangers. Some notable examples include George and Ira Gershwin, Elton John and Tim Rice, and Duke Ellington and Billy Strayhorn.
Building relationships is important for any successful songwriter. Besides artistic collaboration a songwriter must make contacts within the music industry to obtain paying gigs and get recording contracts.