You state your name and request. You make a clear and concise case. And then, after the gate agent informs you that your chances of making it onto this flight are on par with the possibility that a dinosaur will spontaneously reanimate and teach himself to fly an airplane, you nod empathically, say something like “Well, I’m sure we can find a way to work this out,” and step just to the side of the agent’s kiosk.
You must stand quietly and lean forward slightly, hands loosely clasped in a faintly prayerful arrangement. You will be in the gate agent’s peripheral vision—close enough that he can’t escape your presence, not so close that you’re crowding him—but you must keep your eyes fixed placidly on the agent’s face at all times. Assemble your features in an understanding, even beatific expression. Do not speak unless asked a question. Whenever the gate agent says anything, whether to you or other would-be passengers, you must nod empathically.
Continue as above until the gate agent gives you your seat number. The Kindly Brontosaurus always gets a seat number.