To hang objects on cement block walls, you need to choose appropriate hardware. Plastic anchors or lead anchors can provide a secure hold. Drill a hole slightly smaller than the anchor and insert it securely. The anchor will grip the cement block and hold the screw or nail. Be sure to follow safety precautions, such as wearing gloves and using a drill carefully. Measure and mark the wall precisely before drilling. Use a level or laser level to ensure the object hangs straight. Follow the instructions for the particular type of hardware you are using to hang the object securely and prevent damage to the wall.