I dream about painting. Then just remember the dream and paint.
—Vincent Van Gogh
The secret to good ad-libbing is that it really isn't impromptu at all. It isn't usually just made up, offhand, on the spot, or at the last minute. It is thought about, organized, experimented with, researched, experienced, tried out, and practiced, practiced, practiced till the ideas are part of you, long before you stand to deliver.
Notice that I didn't say written down. The problem with writing anything down is that it often never comes up off of the page. It gets stuck there. Interesting ideas that are never communicated. Only very seasoned actors can make a cold read come alive. And notice, by the time the dress rehearsal comes along, the script has long since been put away and the art comes from the heart.
It's okay to note a list of words or phrases on a 3 x 5 card that will serve as talking points, but don't write down what you want to say and try to memorize it. Talk about it out loud, over and over, until you know it. Speaking is called speaking, not reading. Don't make the mistake of telling your thoughts to the page or scraps of paper and then reading them to your audience.
And even if you are still in the process of becoming a pro, you do have one advantage over people with professional speechwriters. Because you've come up with the words yourself, you know what is there. You cared about saying it. It's often been said that "no one cares how much you know until they know how much you care." Your words must come from the heart. Isn't that where our everyday speaking comes from anyway? From inside. You have an idea, a thought, an emotion that needs to be expressed. It has been said, don't seek to inform; seek to persuade, entertain, or motivate. Good speaking requires passion to make its point!
...And don't be surprised. If there's any chance that you will or could be expected to "say a few words," have them ready beforehand. Years of readying clients for their 15 minutes of fame have shown me how important it is to be prepared, whenever called upon. Far better to leave with prepared remarks that weren't needed than to be asked to say a few words and not be primed to do it intelligently, with grace and good humor.
Also, when you are prepared in advance, you will find that opportunities to communicate, with self-confidence, will find you. Audiences are looking for speakers, followers for leaders.
Every public address needs a point of view. It's more than a topic, it's your opinion, your take, your advice; in short, the spin you put on your subject.
Like the perfect quote or sound bite, every word gives meaning to the whole and must have reason to be there. Do not go off on tangents. Not only do the words need a reason to be there, so does the speech. What is its reason for being? What job do you want it to do? What do you need to say to make that happen?
What do you want the people to know? What can you contribute to the moment?
Organize your material in a way that the audience can absorb it, not just hear it. A Zen Master often reminded his students that they would forget the lessons until they remembered the stories. Aesop did it with his famous fables. Who can forget the moral of slow and steady wins the race from The Tortoise and the Hare, of union gives strength from The Bundle of Sticks, or beware lest you lose the substance by grasping at the straws from The Dog and the Shadow?
Be thankful for a captive audience. The next time you are called upon to speak spontaneously, welcome the fact that you won't be interrupted by an interviewer, a therapist, and, hopefully, not even a cell phone.