Nginx works as a front end server, which in this case proxies the requests to a node.js server. Therefore you need to setup an nginx config file for node.

This is what I have done in my Ubuntu box:

Create the file yourdomain.com at /etc/nginx/sites-available/:

vim /etc/nginx/sites-available/yourdomain.com

In it you should have something like:

# the IP(s) on which your node server is running. I chose port 3000.
upstream app_yourdomain {
    server 127.0.0.1:3000;
    keepalive 8;
}

# the nginx server instance
server {
    listen 80;
    listen [::]:80;
    server_name yourdomain.com www.yourdomain.com;
    access_log /var/log/nginx/yourdomain.com.log;

    # pass the request to the node.js server with the correct headers
    # and much more can be added, see nginx config options
    location / {
      proxy_set_header X-Real-IP $remote_addr;
      proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
      proxy_set_header Host $http_host;
      proxy_set_header X-NginX-Proxy true;

      proxy_pass http://app_yourdomain/;
      proxy_redirect off;
    }
 }

If you want nginx (>= 1.3.13) to handle websocket requests as well, add the following lines in the location / section:

proxy_http_version 1.1;
proxy_set_header Upgrade $http_upgrade;
proxy_set_header Connection "upgrade";

Once you have this setup you must enable the site defined in the config file above:

cd /etc/nginx/sites-enabled/ 
ln -s /etc/nginx/sites-available/yourdomain.com yourdomain.com

Create your node server app at /var/www/yourdomain/app.js and run it at localhost:3000

var http = require('http');

http.createServer(function (req, res) {
    res.writeHead(200, {'Content-Type': 'text/plain'});
    res.end('Hello World\n');
}).listen(3000, "127.0.0.1");
console.log('Server running at http://127.0.0.1:3000/');

Test for syntax mistakes:

nginx -t

Restart nginx:

sudo /etc/init.d/nginx restart

Lastly start the node server:

cd /var/www/yourdomain/ && node app.js

Now you should see "Hello World" at yourdomain.com

One last note with regards to starting the node server: you should use some kind of monitoring system for the node daemon. There is an awesome tutorial on node with upstart and monit.

HTTP Solution

From the documentation, "the right way is to define a separate server for example.org":

server {
    listen       80;
    server_name  example.com;
    return       301 http://www.example.com$request_uri;
}

server {
    listen       80;
    server_name  www.example.com;
    ...
}

HTTPS Solution

For those who want a solution including https://...

server {
        listen 80;
        server_name www.domain.com;
        # $scheme will get the http protocol
        # and 301 is best practice for tablet, phone, desktop and seo
        return 301 $scheme://domain.com$request_uri;
}

server {
        listen 80;
        server_name domain.com;
        # here goes the rest of your config file
        # example 
        location / {

            rewrite ^/cp/login?$ /cp/login.php last;
            # etc etc...

        }
}

Note: I have not originally included https:// in my solution since we use loadbalancers and our https:// server is a high-traffic SSL payment server: we do not mix https:// and http://.

To check the nginx version, use nginx -v.

Strip www from url with nginx redirect

server {
    server_name  www.domain.com;
    rewrite ^(.*) http://domain.com$1 permanent;
}

server {
    server_name  domain.com;
    #The rest of your configuration goes here#
}

So you need to have TWO server codes.

Add the www to the url with nginx redirect

If what you need is the opposite, to redirect from domain.com to www.domain.com, you can use this:

server {
    server_name  domain.com;
    rewrite ^(.*) http://www.domain.com$1 permanent;
}

server {
    server_name  www.domain.com;
    #The rest of your configuration goes here#
}

As you can imagine, this is just the opposite and works the same way the first example. This way, you don't get SEO marks down, as it is complete perm redirect and move. The no WWW is forced and the directory shown!

Some of my code shown below for a better view:

server {
    server_name  www.google.com;
    rewrite ^(.*) http://google.com$1 permanent;
}
server {
       listen 80;
       server_name google.com;
       index index.php index.html;
       ####
       # now pull the site from one directory #
       root /var/www/www.google.com/web;
       # done #
       location = /favicon.ico {
                log_not_found off;
                access_log off;
       }
}