The following, taken from the default configuration of our LEMP Application image does this.

        location / {
                # First attempt to serve request as file, then
                # as directory, then fall back to displaying a 404.
                try_files $uri $uri/ =404;
                # Uncomment to enable naxsi on this location
                # include /etc/nginx/naxsi.rules
        }

        error_page 404 /404.html;
        error_page 500 502 503 504 /50x.html;

Any page not found will instead display the content of /404.html (while the address bar remains as is).

Any 50x error will return /50x.html