Making an off the cuff speech means, that one's speech is spontaneous and without any preparation. Of course, such a speech can never be perfect. But you can improve your spontaneity with very specific techniques and still make a nice speech with zero to little preparation time. How do you do that?
There is always a reason for making an off the cuff speech. For example if someone issues a topic spontaneously. When it comes to topics, there is always a crucial term to which you can cling — at least in the beginning minutes. Imagine, somebody says to you: "Just talk briefly about marrying!" — Here you could pick out the word "briefly" and talk about the fact that you can not "talk briefly" about such topics and then argue in detail.
Digress! You accept the topic, talk about it for a moment, and slowly but surely change the subject. In the wedding example above, you could say that besides marrying, there are other great life choices, such as family planning and home buying — and then focus on this topic and talk about buying a home for instance.
Irony! Every topic can be tackled ironically. So in the above example regarding marrying, talk that marriages are not working anymore after statistically 6 years — and make funny guesses about why.
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