There really are 77 Dream Songs. Each one is 18 lines long and divided into 3 stanzas.
The songs trace the life of Henry as told by himself, from several different points of view, and by his unnamed friend who calls him Mr. Bones.
John Berryman has said that he is not Henry, although most people don't believe him. Berryman lost his father to suicide and Henry's life seems forever burdened by "a departure" that's mentioned in Dream Song #1.
One important thing to remember is that Henry often speaks in the first and third person, even within the same line: "I don't see how Henry, pried / open for all the world to see, survived." Henry is observing himself.
In Dream Song #1 we are introduced to a sad but surviving Henry, himself surprised that he's still alive.