This is the code for walking.

Quad.ino

//Arduino provides a set of prebuilt code to run servos. To bring it into our code, we use this command.
#include <Servo.h>

//A class is a collection of differnet data and functions you can use to make coding more conveinent. In this case, we 
//make a class that holds every servo on our robot so we can easily control it
class ServoManager{
  public:
    //Every servo on the robot is created in our class
    Servo FrontRightThigh;
    Servo FrontRightKnee;

    Servo BackRightThigh;
    Servo BackRightKnee;

    Servo FrontLeftThigh;
    Servo FrontLeftKnee;

    Servo BackLeftThigh;
    Servo BackLeftKnee;
  
    //We define a function which will be run at the start.
    void setup(){
      //To start using the servos through the servo library we brought in early, we have to use the 
      //attach command on servos. The attach command takes in the physical port the Servo's signal wire is attached to.
      //We go through every servo, using the attach command passing in the port the servos are attached to
      FrontRightThigh.attach(2);
      BackRightThigh.attach(3);
      FrontLeftThigh.attach(4);
      BackLeftThigh.attach(5);

      FrontRightKnee.attach(8);
      BackRightKnee.attach(9);
      FrontLeftKnee.attach(10);
      BackLeftKnee.attach(11);

    }
    //Here we make a function that takes 8 different numbers, representing the 8 different angles of the servos.
    //The function then takes those 8 numbers and uses the Servo's built in function, write() which takes in an angle to rotate the servo,
    //and uses that command on each of the servo with the corresponding number that was passed in. 
    //This function is used to change the servo's rotations on the quadruped.
    void writeLegs(int FRT, int BRT, int FLT, int BLT, 
                  int FRK, int BRK, int FLK, int BLK ){

                    FrontRightThigh.write(FRT);
                    BackRightThigh.write(BRT);
                    FrontLeftThigh.write(FLT);
                    BackLeftThigh.write(BLT);

                    FrontRightKnee.write(FRK);
                    BackRightKnee.write(BRK);
                    FrontLeftKnee.write(FLK);
                    BackLeftKnee.write(BLK);
    }

};

//here we make the ServoManager object, calling it Manager
ServoManager Manager;

void setup(){
  //Using setup() which is called once, we use the setup() function we defined above, attaching all the servos
  Manager.setup();
}

void loop(){
  //And this is where the robot starts to move! Using the writeLegs() command we made above, we pass in different sets of numbers
  //To change the rotation of each servo. We then wait using the delay command which takes in the number of milliseconds to wait
  //We string these together to have the robot move its legs!
  Manager.writeLegs(90,90,90,90,90+30,90-35,90-30,90+35);
  delay(1000);
  Manager.writeLegs(60,90,110,90,90+15,90-35,90-30,90+35);
  delay(5000);
  Manager.writeLegs(90,60,110,90,90+30,90-65,90-30,90+35);
  delay(1000);
  Manager.writeLegs(70,60,110,90,90+30,90-65,90-30,90+35);
  delay(1000);
  Manager.writeLegs(70,60,110,120,90+30,90-65,90-30,90+35);
  delay(1000);
  Manager.writeLegs(90,90,90,90,90+30,90-35,90-30,90+35);
  delay(1000);
}