I've done this repair for lots of people so I figured I'd show how I do it. Sometimes the headphone jack breaks off and there is a long peg left you can grab with very small needle nose pliers. Most of the time the jack breaks off way down in the jack socket so there's nothing left to grab, even if you could get pliers small enough to fit in there. This technique will work even if the jack is broken off all the way at the base.
This procedure is pretty simple and only takes a couple of minutes- but it does require steady hands!