What information are you trying to retrieve? Some of it will be backed-up automatically, unless you have chosen not to. Some may be backed-up if you specifically chose to do so. Some of it you can copy over USB if you can get the screen unlocked (which will depend on what exactly is broken: display, touch function or both) or have usb debugging enabled.
In short, tell us exactly what the state of the screen/phone is and what you are trying to retrieve. Also if you can't afford to repair the screen what device do you plan to retrieve them to?