Stop and secure the workpiece to prevent movement
Use a rubber band or thick abrasive material to increase grip, then try turning counterclockwise
Try a correctly sized screwdriver with firm downward pressure
Use a screw extractor set (drill pilot hole, then turn extractor counterclockwise)
Create a new groove with a Dremel or rotary tool and use a flathead screwdriver
Drill out the screw head, then remove the remaining shank with pliers or a tap-and-drill method
Use left-hand drill bits to drill into the screw and back it out
Heat the surrounding material (carefully) to loosen thread-locking compounds, then try removal
Apply penetrating oil and wait, then attempt removal again
Use locking pliers (vise-grips) to grip the exposed screw shank and turn counterclockwise
If the screw is still partially accessible, try gripping with needle-nose pliers and turning counterclockwise
Remove the surrounding component to access the back side, then hold the nut or use a wrench to back it out
If nothing works, drill and replace the screw, then repair/patch the damaged hole if needed