You will have to create a web server first, try express.
then you can use something like sockets.io to communicate from the server to your client web page.
then on the webpage you must handle the messages to display them (angular, or maybe just jQuery) - basically on tweet you will send a message from your server to the client web page through socket.io, then your dront end javascript will get the message, parse it and decide how to display it.
Have a look at Sails.js, it's basically express with sockets integrated and a few more things
edit
say you export your server in server.js,
var http = require('./server.js');
var io = require('socket.io')(http);
stream.on('tweet', function (tweet) {
io.sockets.emit("new tweet", {
text: tweet.text,
by: tweet.user.screen_name,
date: tweet.created_at,
counter: counter++;
});
});
require('socket.io')(http) starts the "socket manager" on your server (and also publishes the js client side code for it), so clients can connect to your server through sockets.
io.sockets.emit will send a message to all connected clients.
on your web page you must have something like this
<div id="tweets"></div>
<script src="/your/js/jquery.js"></script>
<script src="/socket.io/socket.io.js"></script>
<script>
var socket = io();
socket.on("new tweet", function(tweet) {
$('#tweets').append('tweet: ' + tweet.text + '<br>');
$('#tweets').append('by:' + ' @' + tweet.by + '<br>');
$('#tweets').append('date:'+ ' ' + tweet.date + ' | ' + tweet.counter + '<br>');
});
</script>
the library /socket.io/socket.io.js was published by that require('socket.io')(http) from earlier, so we can use it on our clients.
the call io() basically connects to the server, and returns a handle to that connection (socket), we use that to receive all messages from the server, and on each message you can write the contents to the page anyway you want.