How to expose a JS Node Module

I am diving into Node.js and have had success installing express and socket. I was able to make the basic chat program easily. This requires these steps:

In app.js (my Node server)

var server = require('http').Server(app);
var io = require('socket.io')(server);

I included minified socket.io.js file in public/javascripts

In public/javascripts/testchat.js simply call IO like this:

var socket = io();

Then do whatever you want with IO stuff.

---

I've made my own Node.js module but I don't understand how to expose it.

In node_modules/myModule/index.js

module.exports = require('./lib');

In node_modules/myModule/lib/index.js

module.exports = myModule;

function myModule(){
    this.name = "hello";
}

myModule.prototype.test = function(){
    console.log(this.name);
}

I can call this stuff easily in app.js

var myModule = require('myModule');
var myMod = new myModule.test(); //hello

But I don't want this thing to run every time I start the server. I want to to only run when a user accesses a specific page. How do I get from here to there? I know I am missing something... I was expecting to be able to do this:

In public/javascripts/myModule.js

var myModule = myModule(); //myModule is undefined
myModule.test();

Thank you.