The Experimenters Kit for Arduino comes with a guide with many example projects you can build, including example sketches. To save you typing them in you can copy and paste them from here into the Arduino IDE.

Project 1: Controlling An LED

This project uses the "Blink" example included with the IDE so you can open it by selecting File -> Examples -> 01.Basics -> Blink. The code is also provided here for reference:

/*
  Blink
  Turns on an LED on for one second, then off for one second, repeatedly.
 
  This example code is in the public domain.
 */
 
// Pin 13 has an LED connected on most Arduino boards.
// give it a name:
int led = 13;

// the setup routine runs once when you press reset:
void setup() {                
  // initialize the digital pin as an output.
  pinMode(led, OUTPUT);     
}

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

Project 2: Controlling 8 LEDs

Example 1:

int ledCount = 8;
int ledPins[] = { 6, 7, 8, 9, 10, 11, 12, 13 };
int ledDelay = 300;

void setup() {
  for (int thisLed = 0; thisLed < ledCount; thisLed++) {
    pinMode(ledPins[thisLed], OUTPUT); 
  }
}

void loop() {
  for (int thisLed = 0; thisLed < ledCount-1; thisLed++) {
    digitalWrite(ledPins[thisLed], HIGH);
    delay(ledDelay);
    digitalWrite(ledPins[thisLed], LOW);
  }
  for (int thisLed = ledCount-1; thisLed > 0; thisLed--) {
    digitalWrite(ledPins[thisLed], HIGH);
    delay(ledDelay);
    digitalWrite(ledPins[thisLed], LOW);
  }
}

Example 2:

int ledCount = 14;
int ledPins[] = { 6, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 8, 7 };
int ledDelay = 300;

void setup() {
  for (int thisLed = 0; thisLed < ledCount; thisLed++) {
    pinMode(ledPins[thisLed], OUTPUT); 
  }
}

void loop() {
  for (int thisLed = 0; thisLed < ledCount-1; thisLed++) {
    digitalWrite(ledPins[thisLed], HIGH);
    delay(ledDelay);
    digitalWrite(ledPins[thisLed], LOW);
  }
}

Project 3: Reading Digital (On/Off) Input

int ledCount = 14;
int ledPins[] = { 6, 7, 8, 9, 10, 11, 12, 13, 12, 11, 10, 9, 8, 7 };
int ledDelay = 300;
int buttonPin = 2;

void setup() {
  for (int thisLed = 0; thisLed < ledCount; thisLed++) {
    pinMode(ledPins[thisLed], OUTPUT);
  }
  pinMode(buttonPin, INPUT);
}

void loop() {
  for (int thisLed = 0; thisLed < ledCount-1; thisLed++) {
    digitalWrite(ledPins[thisLed], HIGH);
    delay(ledDelay);
    while(digitalRead(buttonPin) == HIGH) {
      delay(10);
    }
    digitalWrite(ledPins[thisLed], LOW);
  }
}

Project 4: Reading Analog (Variable) Input

int led = 11;
int lightLevel;

void setup()
{
  Serial.begin(38400);
  pinMode(led, OUTPUT);
}

void loop() 
{
  lightLevel = analogRead(A0);
  Serial.print("Light level: ");
  Serial.println(lightLevel, DEC);
  digitalWrite(led, HIGH);
  delay(lightLevel);
  digitalWrite(led, LOW);
  delay(lightLevel);
}

Project 5: Dimming LEDs Using PWM

Example 1:

int led = 11;
int brightness = 0;
int delayTime = 10;
void setup() {
  pinMode(led, OUTPUT);
}
void loop() {
  while(brightness < 255)
  {
    analogWrite(led, brightness);
    delay(delayTime);
    brightness = brightness + 1;
  }
  while(brightness > 0)
  {
    analogWrite(led, brightness);
    delay(delayTime);
    brightness = brightness - 1;
  }
}

Example 2:

int led = 11;
int lightLevel;
int ledLevel;

void setup()
{
  Serial.begin(38400);
  pinMode(led, OUTPUT);
}

void loop() 
{
  lightLevel = analogRead(A0);
  ledLevel = lightLevel / 4;
  Serial.print("Light level: ");
  Serial.println(lightLevel, DEC);
  analogWrite(led, ledLevel);
  delay(100);
}

Project 6: Making Things Move With Servos

 
int delaytime=10;
int angle=0; #include <Servo.h> Servo myservo; void setup() {   myservo.attach(11); } void loop() {   while (angle <=180)   {       myservo.write(angle);       delay(delaytime);       angle = angle + 1;   }   while (angle > 0)   {       myservo.write(angle);      delay(delaytime);       angle = angle - 1;   } }

Project 7: RGB LED

int redLedPin = 9;
int greenLedPin = 10;
int blueLedPin = 11;

void setup() {
  pinMode(redLedPin, OUTPUT);
  pinMode(greenLedPin, OUTPUT);
  pinMode(blueLedPin, OUTPUT);
}

void loop()  {
  analogWrite(blueLedPin, random(0, 255));
  analogWrite(greenLedPin, random(0, 255));
  analogWrite(redLedPin, random(0, 255));

  delay(500);
}

Project 8: Drive More Outputs With A Shift Register

int dataPin = 2;
int latchPin = 3;
int clockPin = 4;

void setup() {
  pinMode(dataPin, OUTPUT);
  pinMode(latchPin, OUTPUT);
  pinMode(clockPin, OUTPUT);
}

void loop() {
  for (int currentValue = 0; currentValue < 256; currentValue++) {
    // Disable the latch while we clock in data
    digitalWrite(latchPin, LOW);
    
    // Send the value as a binary sequence to the module
    shiftOut(dataPin, clockPin, MSBFIRST, currentValue);

    // Enable the latch again to set the output states
    digitalWrite(latchPin, HIGH);

    delay(200);
  }
}

Project 9: Making Sounds

int piezo = 8;
int duration = 250;

int notes[] = 
{261, 293, 329, 349, 392, 440, 493, 523, 587, 659, 698, 783, 880};
// frequencies for musical notes - from middle C, D, E, F, G, A, B, C, D, E, F, G, A

void setup()
{
  pinMode(piezo, OUTPUT);
}

void loop()
{
  for (int i = 0; i < 13; i++)
  {
    tone(piezo, notes[i], duration);
    delay(duration);
  }
  for (int i = 11; i > 0; --i)
  {
    tone(piezo, notes[i], duration);
    delay(duration);
  }
}

Project 10: Detecting Vibration and Knocks

Example 1:

int knock = 0;

void setup()
{
  Serial.begin(38400);
}

void loop()
{
  knock = analogRead(0);
  Serial.println(knock);
}

Example 2:

int knock = 0;

void setup()
{
  pinMode(13, OUTPUT);
}

void loop()
{
  knock = analogRead(0);
  if (knock > 10)
  {
    digitalWrite(13, HIGH);
    delay(500);
    digitalWrite(13, LOW);
  }
}

Project 11: Light Input Controlling Sound Output

int lightLevel; 
int piezo = 8;
int duration = 300;

void setup()
{
  pinMode(piezo, OUTPUT);
}

void loop() 
{
  lightLevel = analogRead(A0);
  tone(piezo, lightLevel, duration);
  delay(duration);
}