Get into an example immediately

You will free yourself at once of the necessity to think hard about your next sentence, for experiences are easily recounted even in an impromptu situation.
You will get into the swing of speaking, and your first-moment jitters will fly away, giving you the opportunity to warm up to your subject matter.
You will enlist the attention of your audience at once.

The incident-example is a sure-fire method of capturing attention immediately.

Once we get the body charged up and animated, we very soon will get the mind functioning at a rapid pace. So my advice is to throw yourself with abandon into your talk and you will help to insure your success as an impromptu speaker.