How do I properly shock a pool to kill algae?

Super-chlorinate to the shock level based on your CYA level using a CYA/chlorine chart, not a generic guess. Keep the chlorine high for at least 24 hours until water clears and combined chlorine is zero. Brush surfaces, run the pump 24/7, vacuum to waste, and backwash or clean the filter when pressure rises. Don’t stop early or you’ll have to do it again.