First try taking it to an authorized Apple repair center (either at an official Apple store or 3rd party retailer), that way if they damage the headphone jack trying to get the stuck piece out they will have to pay for further repairs or replacements. If an official repair tech can't/doesn't know how to get it out then try the following: 1) take a small nail and put a tiny (less than a pea size) of Krazy brand glue on the tip. 2) stick it into the headphone jack until you make contact with the broken plug piece. Hold it for 30 seconds then let go of the nail and let the glue cure for 3-5 minutes. 3) then gently pull on the nail and it should bring out the broken plug with it.
A couple of warnings: Make sure you don't use gorilla glue, or another type of glue that expands or don't use too much Krazy glue otherwise the glue could stick to the sides of the headphone jack and the process won't work.