Basic Ajax send/receive with node.js

1. Your request should be to the server, NOT the server.js file which instantiates it. So, the request should look something like this: xmlhttp.open("GET","http://localhost:8001/", true); Also, you are trying to serve the front-end (index.html) AND serve AJAX requests at the same URI. To accomplish this, you are going to have to introduce logic to your server.js that will differentiate between your AJAX requests and a normal http access request. To do this, you’ll want to either introduce GET/POST data (i.e. call http://localhost:8001/?getstring=true) or use a different path for your AJAX requests (i.e. call http://localhost:8001/getstring). On the server end then, you’ll need to examine the request object to determine what to write on the response. For the latter option, you need to use the ‘url’ module to parse the request.
2. You are correctly calling listen() but incorrectly writing the response. First of all, if you wish to serve index.html when navigating to http://localhost:8001/, you need to write the contents of the file to the response using response.write() or response.end(). First, you need to include fs=require('fs') to get access to the filesystem. Then, you need to actually serve the file.
3. XMLHttpRequest needs a callback function specified if you use it asynchronously (third parameter = true, as you have done) AND want to do something with the response. The way you have it now, string will be undefined (or perhaps null), because that line will execute before the AJAX request is complete (i.e. the responseText is still empty). If you use it synchronously (third parameter = false), you can write inline code as you have done. This is not recommended as it locks the browser during the request. Asynchronous operation is usually used with the onreadystatechange function, which can handle the response once it is complete. You need to learn the basics of XMLHttpRequest. Start here.

Here is a simple implementation that incorporates all of the above:

server.js:

var http = require('http'),
      fs = require('fs'),
     url = require('url'),
 choices = ["hello world", "goodbye world"];

http.createServer(function(request, response){
    var path = url.parse(request.url).pathname;
    if(path=="/getstring"){
        console.log("request recieved");
        var string = choices[Math.floor(Math.random()*choices.length)];
        console.log("string '" + string + "' chosen");
        response.writeHead(200, {"Content-Type": "text/plain"});
        response.end(string);
        console.log("string sent");
    }else{
        fs.readFile('./index.html', function(err, file) {  
            if(err) {  
                // write an error response or nothing here  
                return;  
            }  
            response.writeHead(200, { 'Content-Type': 'text/html' });  
            response.end(file, "utf-8");  
        });
    }
}).listen(8001);
console.log("server initialized");

frontend (part of index.html):

function newGame()
{
   guessCnt=0;
   guess="";
   server();
   displayHash();
   displayGuessStr();
   displayGuessCnt();
}

function server()
{
   xmlhttp = new XMLHttpRequest();
   xmlhttp.open("GET","http://localhost:8001/getstring", true);
   xmlhttp.onreadystatechange=function(){
         if (xmlhttp.readyState==4 && xmlhttp.status==200){
           string=xmlhttp.responseText;
         }
   }
   xmlhttp.send();
}

You will need to be comfortable with AJAX. Use the mozilla learning center to learn about XMLHttpRequest. After you can use the basic XHR object, you will most likely want to use a good AJAX library instead of manually writing cross-browser AJAX requests (for example, in IE you’ll need to use an ActiveXObject instead of XHR). The AJAX in jQuery is excellent, but if you don’t need everything else jQuery offers, find a good AJAX library here: http://microjs.com/. You will also need to get comfy with the node.js docs, found here. Search http://google.com for some good node.js server and static file server tutorials. http://nodetuts.com is a good place to start.

UPDATE: I have changed response.sendHeader() to the new response.writeHead() in the code above !!!