"De Daumier-Smith's Blue Period" is what is often called a "frame" story. The beginning and ending of such a story take place outside the action of the central story. The frame can be incomplete – the ending doesn't have to be part of the frame. In Henry James's The Turn of the Screw for example an elaborate frame is set up at the beginning of the story, but the frame (which is a dinner party where scary stories are told) is not closed up at the end.
In the case of "Blue Period" the frame is roughly complete. The inner story deals with the narrator's past situation, while the frame story deals mostly with his present situation.
Frame stories often feature unreliable narrators, and call attention to the fact that they are stories, often heard second or third hand. (This is not the case here.) By framing a narrative the way a framer frames a picture, the author says, "Hey, this is art" as opposed to an author that tries to create a create an accurate picture of reality. This is a trademark of Modernism, as we discuss in "Genre."
So, what is the main frame of "Blue Period"? The death of Bobby in 1947. The narrator got to thinking about old Bobby, which in turn got him thinking about everything that went down in 1939. The story is meant to honor Bobby – something which the narrator doesn't think he did while Bobby was alive. This lets us know that this story is a confession, and prepares us that death might be a major theme. This frame also gives us important information on how to read the story to come. Look at the very first lines of the story:
If it made any real sense – and it doesn't even begin to – […] (1)
As you know, the "it" is the story about to be told. These lines invite us to relax and enjoy the ride, to indulge in something that stands outside the rules of logic. We are also told that the narrator hopes the story is ribald because Bobby was "ribald." Dirty jokes are ribald. This is an invitation to look for dirty jokes while we read.
It also lets us know that the narrator is probably (like many Salinger characters) a vocabulary show-off and that we'll have to look a few words up. We also have the additional frame of the title (as we discuss more fully in "What's Up With the Title?"), which tells us that the story might be a little silly and that it will deal with art and sadness, but that it is meant to have universal appeal.
In the spirit of "Modernism" Salinger is stretching the idea of a frame, highlighting its flexibility. For example, this story is constructed of several different kinds of texts, including newspaper clippings (M. Yoshoto's ad), letters (Jean is a letter-writing maniac), diary entries, cartoons, paintings, and drawings, to name a few. This is one of Jean's favorite pictures:
Occasionally, I still dream of a certain white goose flying through an extremely pale-blue sky, with--and it was one of the most daring and accomplished feats of craftsmanship I've ever seen--the blueness of the sky, or an ethos of the blueness of the sky, reflected in the bird's feathers. […] It made the room--it and one or two other pictures close to it in quality. (22)
Salinger is literally decorating the walls of his story with fine art. This piece described above was painted by M. Yoshoto and it comments on the idea of "blue" in the story. The most obvious meaning of "blue" is sadness, but here it also means freedom. Jean is attracted to it because it suggests that "blue" is something natural; it suggests that his grief (like death itself) is something natural, something we have to experience. This passage also repeats a suggestion found often in the story, that art is a way to cope with grief and sadness.
In addition to the parade of literal pictures the story is organized around a series of dreamlike moments that seem like pictures. A prime example is this moment:
[…]it seemed to me that all the seats from all the buses in New York had been unscrewed and taken out and set up in the street, where a monstrous game of Musical Chairs was in full swing. (4)
We discuss this moment in detail in "Symbolism, Imagery, Allegory." We bring it up here to show that it is a vivid, but open word painting. We aren't given any superfluous descriptions of the street or the crowd – we can all imagine a crowded New York City street, and we all know what bus seats and games of musical chairs look like. It is the artistic arrangement of these elements (bus seats, musical chairs, streets) in a unique and meaningful manner that makes a stunning picture.