Install the dependences:

sudo apt-get install php5-common php5-cli php5-fpm

Install nginx:

sudo apt-get install nginx

Start nginx:

sudo service nginx start

Test that it's working (should see “Welcome to nginx!”)

sudo service nginx stop

In your nginx site configuration (/etc/nginx/sites-available/default), uncomment the lines in the server {} section starting with listen for ipv4 / ipv6 both.

scroll down to where it says location ~ .php { and uncomment lines so it looks like this:

location ~ \.php$ {
  fastcgi_split_path_info ^(.+\.php)(/.+)$;
  fastcgi_pass unix:/var/run/php5-fpm.sock;
  fastcgi_index index.php;
  include fastcgi_params;
}

sudo service php5-fpm restart sudo service nginx restart

Your default web root is located at /usr/share/nginx/www

To install mysql: sudo apt-get install mysql-server php5-mysql

At this point I do not know if this works for a 502 Bad Gateway error but…

fastcgi_buffer_size 128k;
fastcgi_buffers 8 128k;
fastcgi_busy_buffers_size 128k;
fastcgi_temp_file_write_size 128k;

In the server section inside the configuration part:

# unless the request is for a valid file, send to bootstrap
if (!-e $request_filename)
{
   rewrite ^(.+)$ /index.php?q=$1 last;
}