This assumes you have two containers running on the same Docker network, where one container was built from the nginx image and the other container was built from the php:fpm image. 

The docker container ls command can be used to ensure the containers are running.

~]# docker container ls -a
CONTAINER ID   IMAGE                 COMMAND                  CREATED        STATUS        PORTS                                                                                                                                                 NAMES
8e894ff6f352   php:fpm               "docker-php-entrypoint"   29 hours ago   Up 29 hours   0.0.0.0:9000->9000/tcp                                                                                                                                php-fpm
24bcf99fc7bc   nginx                 "/docker-entrypoint.sh"   29 hours ago   Up 29 hours   0.0.0.0:80->80/tcp, 0.0.0.0:443->443/tcp

Let's say the server block in the /etc/nginx/conf.d/default.conf file in the nginx container contains the following. Notice that the document root directory is /var/www/html.

AVOID TROUBLE

Ensure the root directive is not defined inside of a location block.

Ensure DNS is able to resolve server_name to the Docker system that contains the PHP container otherwise the PHP file will be downloaded instead of being presented in the browser.

server {
    listen       80;
    server_name  stage.example.com;
    root         /var/www/html;
    index        index.html index.php;

    location / {
        try_files $uri $uri/ /index.php;
    }
}

In this example, both the nginx and PHP FPM containers will need the same exact files located at /var/www/html in each container, thus you'll almost always want the files to reside somewhere on your Docker system, and then to use the --volume option to mount the files on your Docker system to /var/www/html in the Nginx container..

docker run
--publish 80:80
--volume /path/to/html/files:/var/www/html
--volume /path/to/default.conf:/etc/nginx/conf.d/default.conf
nginx

And also in the PHP FPM container.

docker run
--volume /path/to/html/files:/var/www/html
--volume /path/to/www.conf:/usr/local/etc/php-fpm.d/www.conf
php:fpm

Ensure /usr/local/etc/php-fpm.d/www.conf in the PHP container has the following.

listen       = /run/php-fpm/www.sock
listen.owner = www-data
listen.group = www-data
listen.mode  = 0660

You will need to append a location block to the default.conf file for PHP. 

• Notice in this example that fastcgi_pass unix:/run/php-fpm/www.sock, an exact match of the listen directive in the www.conf in the PHP container.
• Notice the fastcgi_param directive contains $document_root$fastcgi_script_name. In this example, $document_root is /var/www/html. This means that both the nginx and PHP FPM containers will need the same exact files mounted to /var/www/html. $fastcgi_script_name will be the name of the PHP file that is being requested. For example, if requesting www.example.com/phpinfo.php, then $fastcgi_script_name will be phpinfo.php.

server {
    listen       80;
    server_name  stage.example.com;
    root         /var/www/html;
    index        index.html index.php;

    location / {
        try_files $uri $uri/ /index.php;
    }

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