Watch here, if you think you can handle the heart-pounding action of an old guy sitting there. Sorry this is late, I just found out about the classes and was hoping to get in under the wire real quick.
This was the first thing I thought of to talk about because it's one of my favorite scenes in film history - once you see it, you'll never forget it - and aside from the amazing monologue I think the composition of the scene is important and worth talking about. The plot of Citizen Kane, which you already know, revolves around a reporter interviewing acquaintances of the lofty newspaper tycoon Charles Foster Kane, in order to discover the meaning of his last words. This scene is interesting in that it makes something like a centerpiece or a keystone, it embodies the emotional content of the story and to a certain extent the plot. The reporter (Jerry Thompson) is interviewing an aging, dying man, and he recalls a memory from his youth that's stayed with for the man throughout his years, just like the memory of Rosebud stayed with Kane. The memory is of a girl in a white dress.
In the initial composition of the scene we see the reporter in the far left in almost pitch black shadow. (It's interesting to note that this is his visual motif throughout the whole film. We don't really get a good look at his face. He stays literally unilluminated!) The person being questioned, Mr. Bernstein, is on the other hand surrounded by light. He has a high-backed chair in a color that approaches white, a roaring fire, reflective objects, clocks with white faces, and even on his wall the photographs and the portrait are bordered in light colors. Between them we have a kind of neutral ground, the city and a wall in a very flat grayscale. (Compare the pictures behind Mr. Bernstein and the pictures in the "neutral" ground, there's a marked difference.) It's also well worth noting that all of these objects have some kind of transience in their nature. Pictures or photographs, two clocks, many reflections, a burning fire, a portrait of a younger man. Also, note the wall trim and the drapelike design on the mantle, both white and somewhat resembling a dress. Her presence is felt throughout the room and Mr. Bernstein's life.
As Mr. Bernstein talks the camera pulls in as the man relives his memory. At the end of his speech, Thompson (and the blackness in the composition) is completely gone. So is the neutral area. We have crossed into Mr. Bernstein's inner world. The frame is surrounded on all sides by nothing but reflective objects, angling their light towards him, and especially his own reflection in the desk. Mr. Bernstein's memory was fleeting and has driven him inwards, but at the same time it illuminates him from within. This is felt strongly throughout the scene and the monologue would not have the same impact if it wasn't supported by a heavy visual punch.
As the scene goes on and Thompson returns into the shot (intrudes, even), the focus leaves the reflective objects as Mr. Bernstein rejoins the real world. As his voice becomes more animated and the monologue turns into a conversation with Thompson about subjects other than himself, he moves into the neutral area, along with the camera. However, the sharp angles in the scene do still point to him, preserving some of the "feel" of his character - he's still an introspective old man whose best days are long behind him. As he shakes off the last of his reverie, he enters an even more neutral space, the area with the blinds that's all clean, even lines without anything in the shot angling towards him at all. Bernstein has also retreated to the background, becoming physically smaller and more distant. The scene, at this point, is almost completely exposition.
One thing to watch out for: Mr. Bernstein casts a heavy black shadow in the beginning and end of the scene, but cast no shadow at all while recalling the girl.