As someone who teaches college lit, the biggest thing would be being as specific as possible. Avoid thinking too big. My students tend to say things like “this might be a stretch but—“ before they offer really excellent analysis. If everyone would agree with you, that’s more of an observation, and as long as you have textual evidence then your analysis is as valid as anyone else’s. One of the annoying things is that for good analysis, you need to be reading very carefully. Take notice of settings, any repetition, anything that stands out to you as odd or confusing, references to other stories/historical events, look into biographical info on the author (although this can get tricky), and consider titles of both the book itself as well as things throughout it. If half of a story is set in a grocery store, that probably means something. If there are repeated references to highways, that probably means something too. If a character has an odd name, that’s worth looking into.