How do you use iterators for a class member vector?

Declaring a container member in a class does not make the class a container, nor does it create a container for the class.

Your LongNumber class does not have a member called container. You have to either write an accessor function:

class LongNumber
{
    private:
        vector<int> number;
	public:
		vector<int>& container();
};

ostream & operator <<(ostream & os, LongNumber & along)
{
    for(std::vector<int>::iterator i = along.container().begin(); i != along.container().end(); ++i) 

or make it a public member:

class LongNumber
{
	public:
        vector<int> number;
};

ostream & operator <<(ostream & os, LongNumber & along)
{
    for(std::vector<int>::iterator i = along.number.begin(); i != along.number.end(); ++i) 

or provide access to the beginning and end iterators:

class LongNumber
{
    private:
        vector<int> number;
	public:
		vector<int>::iterator begin()
		{    
		    return number.begin(); 
		}	
		vector<int>::const_iterator begin() const
		{    
			return number.begin(); 
		}	
		vector<int>::iterator end()
		{    
		    return number.end(); 
		}	
		vector<int>::const_iterator end() const
		{    
			return number.end(); 
		}	
};

ostream & operator <<(ostream & os, LongNumber & along)
{
    for(std::vector<int>::iterator i = along.begin(); i != along.end(); ++i) 

Note that I've changed the type in the loop from std::vector<LongNumber> to std::vector<int> here. The code in the examples above will iterate over the elements of the member container of your along variable.