Your local hardware store should carry screw extractors that are designed for this purpose. They might all be too big though for tiny screws that Apple uses, in which case you might need to check Amazon or Newegg for smaller screw extractors designed for electronics.
An old and well-tested trick is to use glue. True, with multiple screws it will be tedious, and eat up a handful of screwdrivers. But you're going to have to replace the screws anyway, unless this is a one-shot to get at something inside that you want out.
In case you think I'm joking -- I'm not. You're going to glue the tip of the screwdriver to the screw's head, which will then turn.