Both, Ian and Peter make some valid points in their earlier comments; true improvisation is just that, you have "nothing" and you IMPROVISE and thus, we end up with classic bits of business like the Zombie Baked Potato (I'm not kidding... it's amazing what you can do with a fork, napkin and spud).
BUT, in order to reach the skill level of being an effective improvisation artist you must have done the requisite course of study and practice. In my experience that means you have a strong working knowledge of slight-of-hand (for magicians) and various "hands-off" bits should you be a mentalist/mind reader (one of the reasons I stress the importance of being a solid Reader and Muscle Reader).
I know that magicians have a Boy Scout mentalist of "Being Prepared" and thus, have their pockets stuffed full of gimmicks, gadgets and props before they leave the house. Such IS NOT true "Improvisation" but rather, wise planning if you are heading out to setting in which the request to "do something" comes forth. But being overly dependent on such things can neuter you quickly when you show up unprepared and get a similar request. The only solution is to constantly play and experiment with every little odd & end you happen across well before hand...
Have a Solid Working Knowledge of Sleights that can be used with most any common item you are likely to find laying around.
The next step is to work things out in your head as to what you can do with those items outside of showing off your dexterity... while I believe one can have fun doing a two minute cigarette manipulation routine the challenge you face is what to do with a borrowed cell phone or two... perhaps a pocket full of change or borrowed bill?
What can you use that's just randomly laying about, to secretly create this or that gimmick such as an impromptu TT or even a Top-it?
What can you do with a 10-12 inch length of hair and how would you go about getting that strand or two? Is there a common means by which to simply steal out a dark colored thread from off your person or some nearby object?
Nearly 30 years ago I remember a bushy headed bucked toothed, pimpled face skinny guy in Chicago who, in my opinion, was the Master of solid Improvisational magic. His name was Bill Malone and believe it or not, in those days he might have weighed 98 pounds soaking wet. But Bill, like many of the "kids" tied to Izzy Rizzy's House of Tricks and the Bit O'Magic dinner club had a couple of old salts that pushed them constantly, challenging everyone to THINK and be creative... to NOT rely on the standard store bought devices unless we were actually at a paying gig where such things would be more appropriate.
I believe this very old course of thinking is why so many magicians fall in love with Playing Cards and refuse to believe that the general public don't hold the same fascination... or, to be more "correct"... we don't want to believe that we bore folks to death by doing nothing but card trick after card trick.
Before you go there... yes, there are exceptions to that rule but I can assure you that well over 90% of those involved in magic are NOT as entertaining with a pack of pasteboards as was Martin Nash or Michael Ammar, etc.
By all means, know a minimum of six solid card routines you can do with a seriously abused deck of cards... I say this in that most borrowed decks you find at home or in the pub have been beat to hell and back and for that reason they wont be as smooth and easy to work with as a crisp deck. Again, the idea of genuine improvisation is to be prepared to work with whatever is available NOT to have a deck of cards in your pocket 24/7 "just in case". Believe it or not, it actually works against you when it comes to public perceptions.
In regards to classic stuff, you need to know your coins and how to work with those of small as well as large size as well as how to do certain routines without devices (gaffed coins)... or for that matter (since I'm speaking of the classics) being able to do a Cup & Ball routines using the coffee/Tea cups you find at the diner and some wadded up napkins...
My point is to simply prepare yourself by knowing your basics and how to creatively apply them along side certain covert antics that allow you to "cheat" just a bit...
