If you could explain a little more about what you've already tried, it makes it easier for people help track down your problem.

Assuming you followed this tutorial, the first change is to make sure that you create a seperate database and datbase user for both sites. Make sure you also use the right ones in each site's wp-config.php file.

Assuming that the root blog is installed in /var/www/html and the sub-blog is installed to /var/www/html/subdirectory, edit your /etc/nginx/sites-enabled/wordpress file to look like:

server {
        listen 80 default_server;
        listen [::]:80 default_server ipv6only=on;

        root /var/www/html;
        index index.php index.html index.htm;

        server_name your_domain.com;

        location / {
                try_files $uri $uri/ /index.php?q=$uri&$args;
        }

        location /subdirectory {
                try_files $uri $uri/  /subdirectory/index.php?q=$uri&$args;
        }

        error_page 404 /404.html;

        error_page 500 502 503 504 /50x.html;
        location = /50x.html {
                root /usr/share/nginx/html;
        }

        location ~ \.php$ {
                try_files $uri =404;
                fastcgi_split_path_info ^(.+\.php)(/.+)$;
                fastcgi_pass unix:/var/run/php5-fpm.sock;
                fastcgi_index index.php;
                include fastcgi_params;
        }
}

You should be all set to go. If you run into any issues, let us know!

Andrew you got it, you are the BEST!
Thank you !!!