I mentally divide discussion of novels into three stages, though there is often overlap, depending on the novel. The first stage is acclimation, when we're figuring out what's going on. The second stage is the deepening of analysis, when we talk about narrative techniques and themes. The final stage is resolution.
The three biggest elements of a novel are characters, setting, and conflict, and these are the foci of the first stage.
An activity I often do on the first day is to list all the characters on the board and ask for an adjective for each. Sometimes I will put the students into groups and ask them to "cast" the film adaptation of the novel and explain why they chose a particular actor for a role. At this stage we're trying to figure out how the characters relate to each other, what each character wants, and what stands in the way. [I do the same thing for drama.]
What's the setting? What do we already know about this time or place, outside of what the novel tells us? What attitude does the narration take toward the setting? How do the characters engage with technologies? How do the characters fit into the setting? Is the setting part of their identity? Is it part of the conflict? I often have students draw a map at this stage, though not usually on the first day. I have had students draw maps of Robinson Crusoe's island and of Audley Court, and I have had them trace Jonathan Harker's journey through Europe (a first-day activity).
What are the conflicts? Conflicts are usually, but not always, centered in character relations. Thinking about conflicts separately from characters can get students thinking about societal and environmental conflicts.
The above strategies work well for both fiction and drama. When discussing fiction, we also need to look at narrative technique, which I usually save for the middle stage, unless the book has multiple narrators (like Dracula). Who's the narrator? If it's first-person, why is this person speaking? What does the speaker reveal about him/herself and others? If it's third-person, is it omniscient or limited? Does the narrator seem to have a persona? Does the narrator privilege a point of view? How are up-close scenes balanced with descriptive scenes in which we get to see characters in a larger context? When and why does the narrator "zoom in" or out? How are characters' voices and thoughts represented? Does the narrator "preach" or philosophize on the situation?
This middle stage is also when we look closely at quotes that build certain themes. A good introductory quote activity is to let groups choose a quote that interests them for whatever reason. Assign each group a different chapter. Then have them explain what's going on and why they think the quote is important. (You can then use these quotes on your exam.)
The final stage is resolution. What sort of closure is offered? How/ Have characters changed? Have students again give an adjective for each character and compare the list with the one built on the first day. What conflicts have been resolved? What conflicts remain, or what new trouble looms on the horizon? Fun activities at this stage are (1) to have students create tableaux of important scenes in the book, (2) create the "reduced" 2-minute version of the book, and (3) to have a debate about the issues the book was addressing. (These also work for drama.)