CRUD app for managing customers
Here's are a few things that I noticed.

1

The control and flow of the application needs to be seperated into smaller logical groups.
The customers should be a container and controller for the customers, not the otherway around. 
For example, Customer.prototype.addCustomer should be associated with Customers.prototype.addCustomer, since Customers is a container for customer objects.

2

this.id should be a property inside the Customer constructor. Ideally, the id value should be set to null until it is added to the Customers container.

3

Setting an object's prototype to an object over-writes the entire prototype, which means that you lose the reference to the constructor object.
So it's better if you add values and functions to the prototype one at a time like so.

// ok but you lost a few values.
Customer.prototype = {
    method1: function(){
        //...
    }
};

//best
Customer.prototype.method1 = function(){
    //...
};


4

Pass values to the constructor rather than have the constructor go out and find them.

// ok
var Customer = function(el) {
    this.el = document.getElementById(el);    
    this.first_name = $("#input_first_name").val();
    this.last_name = $("#input_last_name").val();
    this.name = ""
}

// best
var Customer = function(el, firstName, lastName ) {
    this.el = document.getElementById(el);    
    this.first_name = firstName;
    this.last_name = lastName;
    this.name = "";
       this.id;
}   


Here's a free online book to help you to understand MVC
http://addyosmani.github.com/backbone-fundamentals/