What are the dramatic conventions of "The Yellow Wallpaper"?

First, and most simply, we have a protagonist, an antagonist, and a conflict in this story: these are all conventions. The protagonist is the narrator, a woman who has recently had a baby. We might be tempted to view her husband, John, as the antagonist, because he's the one responsible for keeping her in isolation, but that would mean her conflict is only with him, and that's not the case. Really, the narrator's conflict is with all of society and its expectations and treatment of women.
The medical diagnosis of "hysteria"—the disease doctors suggest is affecting the narrator —was vague and diffuse: a catch-all for any time a woman was "overly emotional" or not behaving in a socially acceptable way toward her husband and/or child. In reality, it seems like the narrator has postpartum depression: she talks about her anxiety and feeling that she cannot care properly for her son.  The fact that her husband is a doctor and that another, real-life doctor at the time, Weir Mitchell, is mentioned helps us to locate society as the antagonist. Isolating the narrator from all social interaction or anything that might cause her to become to anxious or stimulated and even keeping her in bed all the time would be common "cures" for "hysteria." Often, women treated in these ways would simply pretend to be better in order to avoid further "treatment," which gave the "treatment" the appearance of working. At any rate, then, the conflict here is one of Character vs. Society.
Second, this story relies a great deal on dramatic irony. Dramatic irony occurs when the audience knows more than a character, and this is a great way to build tension in a text: if we know something the character doesn't, we can often see the writing on the wall, so to speak, before they do. This is what happens in this story. We get clues that the narrator's mental health is declining in a way she does not seem aware of and even that the room she stays in was definitely not for children. She mentions bars on the windows, "rings and things" in the wall (which, frankly, sound like a restraining device), and the fact that the bed is tied down.
The narrator's obsession with the yellow wallpaper is probably the biggest clue: when she begins to think it is alive, that it has intention, this should put us on our guard. We know she is deteriorating, even if she doesn't, and though her husband seems aware of it to an extent, he certainly does not understand how deeply mentally ill she has become. This dramatic irony leads to a catharsis, another convention where all the tension is finally purged as the truth comes out. In the end, when the narrator comes to believe that she is the woman who was trapped in the wallpaper and has escaped, her husband learns the true extent of her illness, and the audience experiences catharsis when all the tension of knowing more than he does is released.