Extract contacts from broken phone?

If the screen stays black because of damage or failure of the lcd, the easiest way to extract any data will be to find a shop that will plug a new screen in temporarily to get the data. In order to move data the device will have to have usb debugging enabled. If you haven't previously connected it to a pc, this will be challenging if not impossible with no image or touch function on the screen. PS if you use a google account check to see if your contacts are stored there. Most of the time they will be there as google saves them unless you tell it not to.