Read the paragraph in question, as well as the paragraph before and after. The surrounding paragraphs often offer context that can be used in determining the purpose of the paragraph you are analyzing.
Highlight keywords in the paragraph that might offer clues as to the purpose of the paragraph. Highlighting keywords and comparing them to surrounding paragraphs for similarities can help link ideas or unified themes between each paragraph. This comparison can also show a lack of commonality, which is just as telling.
Ask yourself important questions. Think about the similarities and dissimilar elements between the paragraph you're analyzing and the surrounding paragraphs. Consider the possibilities of purpose. Ask yourself if the author is simply using the paragraph to shift topics or if the author is building upon a concept already introduced in previous paragraphs. In fiction, ask yourself if an author is using the paragraph to develop back story or the current story. Another possibility in fiction may be the author's attempt to show character.
Examine what you get from the paragraph. This is the most important step. Determine what the paragraph did for you. Ask yourself if a particular bit of information was clarified or if there was a shift of focus within the paragraph that helped you transition from one focus to another. Determining what the paragraph does for you may be what the author intended.