You would write about the atmosphere of a novel the same way that you would write about the atmosphere of a movie. If that helps, great. If not, I'll keep explaining. Think of "atmosphere" as equating with the mood of the piece. Setting and mood go hand in hand and work together for the same end of creating atmosphere (really synonymous literary terms). Atmosphere is expressed as the answer to the question: "How does the novel (or a part of the novel) make you feel?"
Right away that is going to force you to answer the question with adjectives. Does it make you feel happy? Sad? Excited? Creeped out? Tense? Scared? Depressed? Angry? Etc. Once you have narrowed down how the novel makes you feel, you need to explain it. That is how you write about atmosphere. I'll give an example of how I write about atmosphere for The Martian:
- The Martian, by Andy Weir, made me feel tense and apprehensive because of the author's ability to create in my imagination the extreme dangers of being stranded on Mars. The specific descriptions of exactly what would happen if any HAB seals broke were harrowing to say the least, and Weir's ability to make the reader feel as alone as the protagonist really made the atmosphere of the novel quite tense throughout.
In my example, I stated what kind of atmosphere was created, and then I explained (very briefly) why I thought that and how the author did it. You can apply that basic structure to any discussion of atmospheric description of a novel.
To understand what a novel's atmosphere is, lets put "atmosphere" into its usual context first. One atmosphere would be a library. When in a library, the visitor can feel the atmosphere. It starts with the physical: the dusty smell, the dry cold air, the quiet except for the accessional page turn or pencil drop. But there is also an emotional atmosphere as well. The hushed feel of the library can effect the individual, imbue a sense of purpose or diligence. The quiet reserve. Also think about how you would describe the atmosphere of an old graveyard after dark.
Now, take those physical and emotional concepts and apply them to how a book makes the reader feel. Not just in one setting, but throughout. How does the reader feel while reading this, and what causes that?
An example could be Animal Farm. The atmosphere would be considered rustic yet political with a rising sense of dread. To discuss this, the writer would suggest descriptions and phrasing (imagery, tone, and diction) that evoked those responses.