Step One: Are you SURE it's just turning and turning...

SORRY! I have to ask! You'd be shocked how much they come out just by a little gentle encouragement.

As a basic first step and periodically throughout, try shaking, pulling or prying the screw out with your knife, prying tool, etc. This might cause a weakened-enough screw to come out. Try sticking a little Scotch tape over the head and pulling during this stage. No? Proceed to next step.