How's an functional murmur diagnosed?

Auscultation: Auscultation of the heart and echo.

Exclude other reason: A murmur is just an extra sound heard when listening to the heart. Sometimes a murmur may be caused by a structural heart problem, such as a septal defect (a hole between the sides of the heart), valvular heart disease (a tight or leaky valve) or a tight blood vessel. We usually look for these with an echocardiogram (an ultrasound of the heart). If the echo is normal, the murmur is functional.

Murmur : Usually by simply listening by a stethoscope. Sometimes you need an echocardiogram to make sure that it is an innocent murmur not something else