Floating, green algae is easy to kill with the right pool chemicals. While yellow algae can be chlorine-resistant, black algae are actually bacteria. It is easy to ignore the first signs of algae building up with a good old-fashioned scrub and vacuum.
But once there is considerable algae growth, you need to add sanitizers, algicides, test the pH and alkalinity in the pool, and balance the water. When the infection is too heavy, use chlorine shock, clean the pool filter, and finally run the pump for 8 hours straight.