Scheduled speeches make many speakers nervous. Giving a speech without notice is just as nerve-wracking, if not more. In fact, being put on the spot or asked to give an impromptu speech can cause the speaker to freeze up and draw a mental blank on any topic. Reduce the anxiety and nervous behavior often associated with impromptu speeches by continually working on improving your public speaking skills even when you don't anticipate giving a speech.
Prepare for impromptu speeches indirectly. Expect that you may be asked to speak on topics you are considered knowledgeable on or are an expert on. Be prepared to speak on these topics without notice. Rarely, if ever, will someone ask you to give a speech on something you don't know anything about.
Keep up to date on the news and events that pertain to your areas of expertise. Chances are your expertise keeps you interested in related news anyway. It will be helpful to be current in an area you may be asked to speak on or knowledgeable if asked your opinion on a recent event, in light of your expertise on the subject.
Ask for a moment to mentally prepare for a speech when put on the spot. While you may not know a speech is coming, once you are asked to give one you can delay it for a moment to collect your thoughts. Mentally map out some main points on the topic you have been asked to speak about.
Remain cool and collected, avoiding panic. Use the fact that the speech is impromptu to your advantage by making an opening joke about being put on the spot. Or if you fumble words, joke that your mind has not yet caught on that you are giving a speech.
Engage the audience by telling them what you plan to say, as you put the plan together in your head. Then go into speaking about the items you said you would speak on. Outlining them at the beginning will prime you for speaking on them more freely and in detail.
Build your confidence in your ability to speak by seeking out speaking opportunities rather than avoiding them. Join a public speaking club like Toastmasters or practice with peers. This way, when asked to speak on the spot, you will be well practiced in general.