The active buzzer has built-in electronics that produces the buzzer sound. For this reason it will sound when power is connected to it and does not need any external electronics or an Arduino for it to produce a sound.
The simplest way to test the buzzer to see that it is working is to connect a 5V power supply that can deliver 30mA or more across its pins. When the buzzer is connected to 5V it should sound.
5V from an Arduino can be connected to the buzzer as shown in the image below. No Arduino sketch is necessary as the Arduino 5V is used directly for testing purposes.