What do literary critics do when they make interpretations?

They give their opinions on the deeper meanings of a story.

Literary critics read the entire text and start analyzing it based on several things: the figures of speech, the historical context of the text, the author's background, the style, the era, etc. and then start basing their opinions. All of these things together are combined into a critic's opinion about a particular text, and they have to take all of these into consideration whilst trying to find the deeper meaning.