When creating an instance of a Javascript "class," is there a way to structure the object such that all methods may be accessed?

Is there a way to create an object in Javascript such that all of its methods are available to the constructor?

You can call any method once it's been created. In your example, there are two issues:

1. You haven't created the method yet

2. You are calling it incorrectly — in JavaScript, using the object qualifier (this. within a constructor, usually) isn't optional as it is in some other languages

If you define methods on the constructor function's prototype property, provided those assignments happen before the call to the constructor (which is usually true, and there are techniques for guaranteeing it), the methods will be available on this within the constructor. If you create methods within the constructor (as in your example), just create them first.

Here's your example using the constructor's prototype property, which refers to the object that will be used as the prototype of instances created via new:

function Example() {
  var someVar = something;
  var moreState = initializedToSomethingElse; 

  this.verifySomething(); // <== Works
}
Example.prototype.verifySomething = function() {
    // do verify stuff
};

var e = new Example();

Here's an example defining within the constructor that makes use of the fact that function declarations (rather than expressions) are "hoisted" (completed before any step-by-step code runs).

function Example() {
  var someVar = something;
  var moreState = initializedToSomethingElse; 
  this.verifySomething = verifySomething; // <== Note we assign first

  this.verifySomething(); // <== Works

  function verifySomething() {
      // do verify stuff
  }
}

var e = new Example();

If you really don't like doing that assignment before calling it, you could use .call:

function Example() {
  var someVar = something;
  var moreState = initializedToSomethingElse; 

  verifySomething.call(this); // <== Works
  // this.verifySomething();  // <== Would not work

  this.verifySomething = verifySomething; // <== Note we assign after
  function verifySomething() {
      // do verify stuff
  }
}

var e = new Example();

I mentioned above that there are techniques for guaranteeing that the prototype property of the constructor function has been fully fleshed-out before the constructor is ever called. Here's one of them (using a scoping function):

var Example = (function() {
    function Example() {
      var someVar = something;
      var moreState = initializedToSomethingElse; 

      this.verifySomething(); // <== Works
    }
    Example.prototype.verifySomething = function() {
        // do verify stuff
    };

    return Example;
})();

var e = new Example();

With the above, there's no way code outside the containing immediately-invoked scoping function can use Example until after that scoping function has finished, and therefore fully set up the prototype property.