Use the correct-size socket first
Try a six-point socket, not a twelve-point socket
Tap the socket onto the lug nut with a hammer
Use a breaker bar for more leverage
Apply penetrating oil and wait
Try tightening slightly before loosening
Use locking pliers if part of the nut is exposed
Use a lug nut extractor socket
Heat the lug nut carefully if safe to do so
Strike the lug nut with a hammer to break corrosion
Use an impact wrench if available
Remove the wheel for better access if possible
Cut a slot in the lug nut with a rotary tool
Split the lug nut with a chisel or nut splitter
Drill the lug nut off as a last resort
Replace the lug nut afterward
Replace the wheel stud if it is damaged