An extemporaneous speech is a planned speech delivered with the help of notes rather than being memorized word-for-word. It involves identifying the type of question being addressed, such as one of fact, value, or policy, determining the appropriate purpose, and considering all sides of the issue. When preparing, the speaker should reinforce their central thesis across points, capture the idea in one sentence, develop supporting points in an outline, grab attention in the introduction, check that each main point reiterates the thesis with evidence, and conclude by connecting back to the opening.