How do you remove a broken dipstick tube from the engine of a 1995 Pontiac Grand Prix 3.1 L?

Use a magnet at the end of a flexible pole. You have, no doubt, seen the telescoping magnets used to retrieve lost bolts/nuts/misc metal parts sold at the auto parts stores. This concept can be taken a bit further by attaching that magnet to a piece of flexible plastic tubing and flopping it around in the tube. Alternatively, you can remove the oil pan :)