Salinger has written much about the Glass family before, but he fits the back-story in here, in case you missed it. There are seven Glass siblings, starting with Seymour, who is about to get married. Following Seymour we have Buddy, the narrator, then Boo Boo, who is out to sea as a naval ensign, the twins Walt and Waker (both similarly out of the picture at the moment), and the youngest two, Zooey and Franny, who are still living with the Glass parents. The Glass children are a special bunch. As kids, they were all on a radio quiz program called "It's a Wise Child," where they answered questions and impressed the public with their precocity. They are all extremely intelligent and well educated, particularly in the fields of literature, religion, and philosophy. The oldest sibling, Seymour, is largely responsible for educating his younger siblings.
"Roof Beam" takes place in 1942, on the day of Seymour's wedding. (Buddy, narrating from a later vantage point, tells us that Seymour killed himself six years after the wedding.) Since all the rest of the Glass family is abroad or unavailable, Buddy is the only one who can make it to the wedding. He is in the army and so gets a three-day leave to travel to New York for the ceremony. He's been recovering from pleurisy (a painful infection affecting the lungs) and so the trip is a hot, uncomfortable, cough-ridden fiasco.
On top of that, Seymour doesn't end up coming to his own wedding. The bride, Muriel, is taken away in tears, and the various guests (all from her side) are told to take the guest cars over to the reception anyway. Buddy ends up getting into a car with four other guests, much to his own surprise. One of the guests is the Matron of Honor, who spends the entire trip ranting about what a psycho Seymour is. Another is a bride's great-uncle, who is both deaf and mute. Buddy takes great comfort in his silence and Zen-like calm while trying to discern if the angry Matron of Honor actually knows he (Buddy) is Seymour's brother.
In the end it does come out that Buddy is Seymour's brother, but this doesn't stop the Matron of Honor from railing on Seymour all the more. Through her ranting and Buddy's narrative commentary, more of the real story comes out. It turns out that Seymour is a peculiar individual. He's spiritual, socially detached, and in all likelihood suffering Posttraumatic Stress Disorder from his time in the army during World War II.
The Matron of Honor also heard a terrible story that Seymour is responsible for the crooked smile of a very famous actress of the day – supposedly he gave her a bunch of stitches in her face when they were kids together. On the other hand, Seymour's fiancée Muriel is a social, light-hearted girl. Muriel's mother, Mrs. Fedder, thinks that Seymour ought to be psychoanalyzed. Apparently, the night before the wedding, Seymour called Muriel and made her meet him a hotel lobby to talk for several hours. He told her that he was too happy to get married, and that they would just have to put the whole thing off until he felt steadier.
Meanwhile the car with these five guests has been stopped in the middle of the hot city streets to allow a parade to pass. The guests despair, and Buddy invites them all over to his nearby apartment that he and Seymour used to share. There, Buddy discovers that Seymour has been by recently and left out his diary out. We get to see several entries in which Seymour documents his feelings for and interactions with Muriel. He says he loves her dearly, but it's clear that he has great difficulty in relating to anyone, even her.
As the guests mill around the apartment, they find some photos on the wall taken when the Glass children were small. They identify a little girl in the photos with Seymour as Charlotte Mayhew, the famous actress discussed earlier. Muriel's aunt, points out that Muriel actually looks quite a bit like Charlotte. Buddy reels from this information and its "implications."
The Matron of Honor ends up phoning the bride's parents and reports back that everything turned out just fine – Seymour showed up and whisked Muriel away to elope with him. The guests, relieved, bustle out of Buddy's apartment, forgetting about the great-uncle and leaving him alone with Buddy. Buddy, thoroughly drunk at this point from a foray into the liquor cabinet, tells the uncle (who is deaf) the story of how Seymour gave Charlotte all those stitches. It's clear that there was an intense childhood love between the two of them.
"Seymour: an Introduction" is quite a different story from "Roof Beam." The narrator is once again Buddy Glass, but here he is 40 and writing from his isolated home in the woods. This is not as much a short story, he explains, as it is his attempt at describing Seymour to us. The piece is an amalgamation of narrative commentary, digressions, and anecdotes from Buddy and Seymour's childhood. It is not only about Seymour, but about the writing process as well. In particular, "Seymour" is about the difficulty of writing anything final about a person who, in Buddy's words, is too large to fit on paper.
In any case this short story is fragmented, non-linear, and not something we can re-tell for you in a paragraph or two. We can tell you that the piece explores Seymour's own writing – it turns out that he was a prolific poet in his last few years. It also explores his spirituality (Buddy describes him as a "God-knower"), which is actually very much related to his poetry (Seymour wrote a sort of specialized haiku). We hear about the enormous influence Seymour had on Buddy when they were growing up together, especially in the realm of Buddy's own writing. (Seymour was always the first to read and respond to Buddy's work.)
Buddy ends up discussing – somewhat subtly – several of Salinger's other works, which he claims to have written himself ("A Perfect Day for Bananafish" and "Teddy" are discussed. It's possible that Buddy also alludes to The Catcher in the Rye). Buddy admits that he can't help but write about Seymour, even when a story is supposed to be about something else. He references Seymour's suicide without discussing it in detail; he won't be ready for that for another few years, he says.
Though Buddy is primarily talking about Seymour, we learn a lot about Buddy from listening to him narrate. He currently teaches English at a women's college, writes professionally, and lives like a hermit in his little house in the woods. Buddy appears largely cynical throughout the course of the narrative with regard to readers, English students, publishers, critics, and his own teaching. He concludes at the end of "Seymour," however, that the most important thing he does is go into work every day and teach his class of students. It's clear that his optimistic conclusions are the result of Seymour's influence on his character and personal philosophy.