Well, that was easy!
Since the Verbal Machines VM-CLAP1 sensor is an open collector type — that is, it sinks current when triggered — it behaves like a simple button to gpiozero, the Raspberry Pi Python GPIO library. If you attach a callback function to the sensor’s when_pressed event, your Python script will call that function every time it registers a clap.
The wiring is as simple as it could be:

VM-CLAP1: Raspberry Pi:
 ========= =============
 GND → GND
 PWR → 3V3
 OUT → GPIO 4
This example code just prints clap! when the board picks up a ðŸ‘:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Raspberry Pi gpiozero test for
# Verbal Machines VM-CLAP1 clap sensor
# scruss - 2017-06
#
# Wiring:
#
# VM-CLAP1: Raspberry Pi:
# ========= =============
# GND → GND
# PWR → 3V3
# OUT → GPIO 4
from gpiozero import Button
from signal import pause
def clapping():
print("clap!")
clap = Button(4)
clap.when_pressed = clapping
pause()
This is a trivial example, but at least it shows that anything you can do with a button, you can also do with this hand-clap sensor.