Tutorial: Active Buzzer

Buzzers 

Transducer - converts electrical energy into mechanical energy

Two categories: Active and Passive (you have one of each type in your kit)

Active Buzzer is the slightly taller one, with a solid, plastic coat on the bottom and a label that says to remove it after washing.

Only requires an external DC voltage to make it sound (batteries or USB from Arduino)

An active buzzer has a built-in oscillating source, so it will make sounds when electrified.

Can turn it on or off to make various sounds

You can use a 100 Ω resistor with it but its optional.

Uxcell a12081600ux0477 12 mm Diameter DC 5V 2 Terminals Electronic Continuous Sound Buzzer

Use simple code to turn it on and off: 

int buzzerPin = 4;

// the setup function runs once 
void setup() {
  // initialize digital pin 7 as an output.
  pinMode(buzzerPin, OUTPUT);
}

// the loop function runs over and over again forever
void loop() {
  digitalWrite(buzzerPin, HIGH);   // turn the buzzer on (HIGH is the voltage level)
  delay(1000);                       // wait for a second
  digitalWrite(buzzerPin, LOW);    // turn the buzzer off by making the voltage LOW
  delay(1000);                       // wait for a second
}

Another Approach: Write a function

// Buzzer example function for the CEM-1203 buzzer (Sparkfun's part #COM-07950).
// by Rob Faludi
// http://www.faludi.com

void setup() {
  pinMode(4, OUTPUT); // set a pin for buzzer output
}

void loop() {
  buzz(4, 2500, 500); // buzz the buzzer on pin 4 at 2500Hz for 500 milliseconds
  delay(1000); // wait a bit between buzzes
}

void buzz(int targetPin, long frequency, long length) {
  long delayValue = 1000000/frequency/2; // calculate the delay value between transitions
  // 1 second's worth of microseconds, divided by the frequency, then split in half since
  // there are two phases to each cycle
  long numCycles = frequency * length/ 1000; // calculate the number of cycles for proper timing
  // multiply frequency, which is really cycles per second, by the number of seconds to 
  // get the total number of cycles to produce
 for (long i=0; i < numCycles; i++){ // for the calculated length of time...
    digitalWrite(targetPin,HIGH); // write the buzzer pin high to push out the diaphram
    delayMicroseconds(delayValue); // wait for the calculated delay value
    digitalWrite(targetPin,LOW); // write the buzzer pin low to pull back the diaphram
    delayMicroseconds(delayValue); // wait again for the calculated delay value
  }
}