Topic sentences for single paragraph assignments have one purpose: to answer the prompt with an assertion. In most cases, they also include the author's name and title. See this page for advice on structuring assertions.
Within an essay, topic sentences should do three things: (1) transition from the previous idea, (2) define the focus of the paragraph, and (3) support at least part of the thesis. In the examples below, I bolded phrases that transition and italicized phrases that define the focus of the paragraph.
Transitions make it clear how each paragraph builds on the previous paragraph. In the example below, the word "increases" in the second topic sentence shows that it's building on an idea in the first paragraph. The phrase "finally recognizes" in the third topic sentence indicates that there's a shift from the previous paragraph. See this page for lists of transition words and more advanced transitioning strategies.
Defining the focus means clarifying what makes the paragraph different from the others. In the example below, each paragraph focuses on a different part of the story ("Before the party," "During the party itself," "at the very end of the party"). If I were writing a longer essay, I could have broken up the story further (beginning, first half of the party, second half of the party, end).
Most importantly, each paragraph makes an assertion that supports the thesis. It's important to note that individual paragraphs do not independently prove the entire thesis. Paragraphs need to work together to do this. The examples below both trace Rosaura's misunderstanding throughout the story. Some paragraphs just show she believes she is a guest; others show she is actually a maid; some show both. Don't try to prove your entire thesis in every paragraph.
Thesis: In "The Stolen Party" by Liliana Heker, Rosaura misinterprets her role at the party because she believes she is a guest while being treated like a maid.
Topic Sentence #1: Before the party, despite her mother's warnings, Rosaura believes she has been invited to the party as a friend.
Topic Sentence #2: During the party itself, Rosaura's confidence in her role as a guest increases even as Señora Ines assigns her tasks that would normally be performed by a maid.
Topic Sentence #3: Rosaura finally recognizes she was invited to serve the other children at the very end of the party.