True impromptu speaking (as opposed to extemporanous speaking) is sufficiently difficult that some texts recommend that you simply "avoid impromptu speeches whenever possible". Sage as that advice may be, it doesn't help much when you can't avoid having to give one.
Consequently, here are three simple rules for impromptu speaking: Define, Divide, and the "Tell 'em" Rule.
Definition is extremely valuable in rhetoric, especially at the beginning of a speech or essay. Let's say you have to give a brief impromptu speech on Body Piercing. You could give a dictionary type definition of body piercing, but it is unlikely that your audience needs this, or that it would benefit you in any way, other than to take up time. (If the topic had instead been "Cloning Humans," you would benefit considerably from defining cloning to the best of your ability.)
Nevertheless, regardless of whether or not you need to provide any "technical" definitions relating to your topic, it is still important that you define the scope of your speech for your audience. If you are in a situation where you are expected to make an argument about body piercing, you need to define exactly what the controversy is, and say what aspect of this controversy you are going to address.
You could start by saying that you will not talk about pierced ears for women because there is nothing controversial about that in our society today. For that matter, pierced ears are so common among men, as well, that they too are no longer controversial in our society. However, it is the piercing of other body parts, such as noses, lips, tongues, eyebrows, navels, and other portions of the anatomy you might prefer not to discuss, that is controversial today.
If you were to do that, you would have effectively defined (as in delimited, or put a fence around) the part of the topic that you were going to discuss, which serves two important purposes: it prepares your listening audience for what they are about to hear, and it serves as a contract between you and the audience. All you have to do now is make good on your promise, i.e., talk about only that which you just promised to talk about.
Division is also extremely important in rhetoric because it is what prevents any piece of communication from turning into word soup. Clear divisions are essential to an orderly arrangement, and an audience of listeners needs an orderly (even "predictable" is good in some cases) arrangement if they are going to follow your argument or explanation.
The ways to divide a subject are innumerable. For a short argument, a two or three part division is plenty (especially since the "Tell 'em Rule" allows you to use each part two or three times). Some of the classic two or three way divsions are: past, present, future; that was then, this is now; low, medium, high; cost, benefit; financial cost, social cost; civil law, moral law; problem, solution; thesis, antithesis; thesis, antithesis, synthesis; us, them; ideal, real; what we want, what we can get; mind, body; animal, vegetable, mineral. The list can go on forever. However, in impromptu speaking situations, you don't have forever, but have little or no time for composion. So, you must pick a division as quickly as possible and stick to that one.
Back to our example of Body Piercing, you could, after having defined the conrtroversial part of the topic as piercing body parts other than the ear lobes, divide the subject into health considerations and aesthetic or fashion considerations.
If the situation calls for you to make an argument on this controvery, you need to take a stand. Very simply, you can say that this activity is good or bad, wise or unwise, ought to be banned or should be allowed.
Let's say that you think body piercing is okay, within certain limits. You may choose to assert your position early in the speech, and then proceed to argue that certain health risks must be guarded against (which may then entail licensing or certification of piercers) but that beyond basic health considerations, getting pierced is an aesthetic choice that any adult (there's another limitation--you can insist insist that certified piercers work only on people over 18) should be free to make.
You may then feel the need to defend the reasonableness of making such a choice, which you might do by pointing out that despite its seeming "extremeness," it is not that big a deal, and that anyone who regrets getting pierced need only stop wearing whatever jewelry they chose, and the piercing will close right up leaving little or no visible remainder.
Having done that (defined, divided, asserted a position, added qualifiers, addressed one or more opposing views) you have done all you need to do, except recapitulate your argument, which is where the "Tell 'em Rule" comes in.
The "Tell 'em" Rule
An old adage of Speech Communication says, when giving a speech, you should tell 'em what you're going to tell 'em, then tell 'em, then tell 'em what you told 'em. There is more than a kernel of truth in that rule because of the fact that a listening audience cannot go back to an earlier portion of the speech if they get lost. Therefore, it is important that you keep them from getting lost. And the best way to keep them from getting lost is to first give them a map (sometimes called an "Organization Preview) which you do when you "tell 'em what you're going to tell 'em."
Then you tell 'em,
that is, you make good on your contract to discuss the parts of the topic
which you told them you were going to deal with. Finally, you "tell
'em what you told 'em," that is, recapitulate your argument by repeating
what your main points were. By the time you have done all that, you have
done all you need to do. So, instead of running out of things to say in
the time alloted, if you know what you are doing, you will be hard pressed
to get it all done, even if you have very little material to work with.