Install PHP and NGINX on Amazon Linux AMI

Commands.sh

## Install NGINX
## when installing on Amazon Linux AMI, use:
$ sudo yum install nginx -y
## when installing on Amazon Linux 2 AMI, use
$ sudo amazon-linux-extras install nginx1.12 -y

## Install PHP and PHP-FPM
# for PHP version 7.1 use php71 and php71-fpm instead
$ sudo yum install php -y
$ sudo yum install php-fpm -y

## Configure NGINX (see below)
$ sudo nano /etc/nginx/conf.d/default.conf

## Configure PHP-FPM (see below)
$ sudo nano /etc/php-fpm.d/www.conf

## Add NGINX and PHP-FPM service start to boot sequence
$ sudo chkconfig nginx on
$ sudo chkconfig php-fpm on

## Start NGINX and PHP-FPM service
$ sudo service nginx start
$ sudo service php-fpm start

## Add <file>.php to /var/www/html
## Verify configuration via http://www.domain.com/<file>.php

default.conf

server {
	listen 80;
	listen [::]:80;
	server_name www.domain.com domain.com;

	location / {
	    root   /var/www/html;
	    index  index.php index.html index.htm;
	}

	location ~ \.php$ {
	    root /var/www/html;
	    fastcgi_pass   unix:/var/run/php-fpm/php-fpm.sock;
	    fastcgi_index  index.php;
	    fastcgi_param  SCRIPT_FILENAME  $document_root$fastcgi_script_name;
	    include        fastcgi_params;
	}
}

www.conf

## Config associated with PHP-FPM version 7.1
## Comment out the following entries (with ;)
;listen.acl_users = apache,nginx 
;listen.owner = nobody
;listen.group = nobody
;listen.mode = 0666
;user = apache
;group = apache

## Add the following values instead
listen = /var/run/php-fpm/php-fpm.sock
listen.owner = nginx
listen.group = nginx
listen.mode = 0664
user = nginx
group = nginx

The nginx1.12 topic is WAY outdated (and marked as such by the amazon-linux-extras command, if you have the topic enabled. It's hidden if you don't). Use the topic nginx1 instead.