Writers almost always find that they agree or disagree with other writers' ideas. In this type of response, it's your job to consider why you either agree or disagree or both with particular points another writer is making and then to explain to your audience your point of view. An agree/disagree response is not an opportunity to make unsupported claims. You will have to develop reasons for why you agree/disagree using evidence.
Good writers are also good at interpreting what other writers mean. Part of this is because interpretation requires you to imagine possible reasons for the choices that other writers make. Writing an interpretive response can be difficult because you have to think carefully about the kinds of things that might be motivating and directing another writer. This mean that you might have to speculate what another writer's beliefs are or consider the what they seem to be implying by their arguments. Again, relying on evidence can be helpful in creating a solid and interesting interpretive response.
Most writers will have to do some analysis at some point in their academic career. Like the interpretive response, Analyzing another writer's text can help you to learn more about the writer's intentions, but more than likely, it will help you to develop a better sense of whether or not the text is effective. In order to analyze a text, you might have to think carefully about specific elements: who's the audience? what's the main purpose of the text? what type of evidence does the writer use? An analysis might also have you take a close look at the writers tone or style or you might think about how the writer organized their argument. Overall, an analytical response provides your readers with a better understanding of how a text functions and how it attempts to communicate issues to an audience.