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?

 

If you used the Google option to save your pictures to Google Photo's or use Google Drive for other files... then use another computer and log into your Google account. Then anything you saved to those Google account features will be available to copy to any kind or drive you may already own.

The same could be true if you used other cloud based storage options ( Onedrive or some other one )... but you'll need to log into that account using the username/password you'd made for those accounts.

There are no free options to repair anything broken that I'm aware of.