Remove all the water from your birdbath.
Scrub gently at the inner bowl of the birdbath with the scrub brush. If there is prior algae growth, apply a commercial birdbath cleaner and scrub until it is eliminated.
Rinse the bowl thoroughly with clean water to remove all traces of the cleaner. Refill the bath with fresh water.
Add a commercial birdbath water cleaner to the fresh water to discourage future algae growth and help maintain clear water. One example is Microbe-Lift Birdbath Clear.