How is the highness or lowness of a sound determined?

The pitch of a sound is determined by listening to it. Those with what is called perfect pitch can usually tell what the pitch of a given sound is. The rest of us can use simple electronic equipment that can "read" the frequency of a given waveform.

Recall that the mechanical energy we call sound has a pair of basic properties, those being frequency and amplitude. Many different electronic equipments (like an oscilloscope, for one) can be connected to a microphone to determine the pitch of a sound under investigation.