Saving Opportunity and related Contact from single VF page

I am trying to do the following:- 

1) Declaring the object variables

6) Inserting (or Update?) the contact object to the database

Any help with my approach is greatly appreciated!

public with sharing class NewLeadControllerExtension 
{
    ApexPages.StandardController controller;
    public Opportunity oppt {get; set;}
    public Contact cont {get; set;}
    public NewLeadControllerExtension(ApexPages.StandardController controller)
    {
        this.controller = controller;
        oppt = (Opportunity)controller.getRecord();
        oppt.AccountId.Contact.Id = cont.Id;
    }
    public PageReference SaveBoth()
    {
        controller.Save();
        insert cont; 
        return null;
    }
}