Turn the fountain off by unplugging it to stop the pump. Leaving the pump running when you remove the water to clean the fountain can cause the pump to burn out.
Drain the fountain. If the fountain doesn't have a removable plug for draining it, bail the water out with a pail. Soak up any standing water with towels.
Pour white vinegar in the fountain, applying it directly on the areas covered in algae. Brush the algae off with a scrub brush, using a circular motion to remove the algae.
Soak a rag in white vinegar. Use the wet rag to saturate any areas of algae still stuck to the fountain surface. Leave the vinegar on the algae for 10 minutes. Brush the algae off the surfaces.
Wipe the algae debris out of the fountain with a rag. Refill the fountain, dry your hands thoroughly and plug the pump back in.