I need an explanation of Auxiliary operators. I understand that they are not members of a
given class. But how do you use them? Particularly in overloading operators situations.

>But how do you use them? Particularly in overloading operators situations.
All of the friend functions in the following code are auxiliary functions.

#include <iostream>

using namespace std;

class Integer {
public:
  Integer(int init): data(init) {}
public:
  friend ostream& operator<<(ostream& out, const Integer& i);
  friend istream& operator>>(istream& in, Integer& i);
  friend Integer operator+(const Integer& a, const Integer& b);
private:
  int data;
};

int main()
{
  Integer a(10);
  Integer b(5);

  cout<< a + b <<endl;
}

ostream& operator<<(ostream& out, const Integer& i)
{
  return out<< i.data;
}

istream& operator>>(istream& in, Integer& i)
{
  return in>> i.data;
}

Integer operator+(const Integer& a, const Integer& b)
{
  return Integer(a.data + b.data);
}

Auxiliary functions are basically functions that don't need to be member functions (use your own judgement). Sometimes they need access to private members and should be friends, other times they can be written using the public interface of a class.