This segment is written mainly in summary about a chunk of Whitman's younger days working and living in and around New York. Although there isn't much information in the section there are a few instances where Whitman's voice comes through the text.
He describes himself as a "most omnivorous novel reader," which seems to indicate that he read often and chose a wide variety of texts. He goes on to say that he "devour'd everything he could get." This shows that his passion for reading and writing began at an early age. He claims to have been fond of the theater but also says that he witnessed fine performance only sometimes, which could either indicate that only a handful of performances were worth remembering or perhaps that some of time he didn't necessarily enjoy it at all.
He claims his experience teaching in schools was his best experience and held the "deepest lessons in human nature." These years undoubtedly influenced his future works, especially since he indicated that it taught him about human nature.
There was one other moment in the final sentence that i found interesting, Whitman refers to his early attempts at poetry and puts the word poetry in quotation marks. I suppose this is with the intent to leave room for interpretation as to what is even considered poetry and I felt that it might even possibly show a hint of sarcasm with regards to the broad concept of poetry itself.