How to do close reading?
In plainest terms, it's about the ability to analyze and discuss about minute or finer details and analyze so with depth, research, and authority.
As you close read a text, you'll notice more and more details that seem significant, and seem to work together to create meaning. Then, since your understanding of the text's meaning has deepened, more and more details will in turn seem meaningful.
Not very dissimilar to putting a magnifying glass over a bug. As you keep watching more details you start to notice what you missed in the first place.