This is done by keeping one hand straight, placing it under the chin, and 'throwing out' that hand toward the receiver of the gesture.
"Fangul" is not an Italian word, but its probable origins are in the Italian word "Vaffanculo", which means "Go fuck yourself". In Italian culture this gesture means "Chi se ne frega?" or "Who cares?". If done with less intensity, it can also simply mean "No" or "None".
In Italian-American culture, on the other hand, the gesture means "Screw You!". There is a subtle difference between the offensive version of the gesture and the innocuous version. In the "Screw You" version, the fingers are kept stiff and together and the motion is quick and abrupt. In the less offensive "I don't care" version, which has its root in Europe, the fingers fan out and the motion is gentle/nonchalant.