Steps to enable gzip/deflate in nginx server

Edit your nginx.conf file or create a new config file called /etc/nginx/conf.d/static_gzip.conf:
$ sudo vi /etc/nginx/nginx.conf
Add the following in http context:

        ##
        # Gzip Settings
        ##
 
        gzip on;
        gzip_disable "msie6";
 
        gzip_vary on;
        gzip_proxied any;
        gzip_comp_level 6;
        gzip_buffers 16 8k;
        gzip_http_version 1.1;
        gzip_types text/plain text/css application/json application/javascript text/xml application/xml application/xml+rss text/javascript;

Save and close the file. Verify that there are no errors in config file:
$ nginx -t
nginx: the configuration file /etc/nginx/nginx.conf syntax is ok
nginx: configuration file /etc/nginx/nginx.conf test is successful

Restart the nginx server

Type the following command to restart or reload nginx server:
$ sudo service nginx reload
OR
$ sudo systemctl reload nginx
OR
$ sudo /etc/init.d/nginx reload

How do I verify gzip/deflate working or not?

Use the following syntax:
$ curl -I -H 'Accept-Encoding: gzip,deflate' https://your-domain-here/file.css
$ curl -I -H 'Accept-Encoding: gzip,deflate' https://s0.cyberciti.org/assets/auto/cms/wp-content/cache/autoptimize/css/autoptimize_4c2bea242e2386438912dd88773b352c.css
$ curl -I -H 'Accept-Encoding: gzip,deflate' https://www.cyberciti.biz/
Sample outputs:

HTTP/1.1 200 OK
Server: nginx
Date: Sun, 05 Mar 2017 18:45:31 GMT
Content-Type: text/html; charset=UTF-8
Connection: keep-alive
Vary: Accept-Encoding
X-Whom: l1-com-cyber
Strict-Transport-Security: max-age=15768000; includeSubdomains
Link: ; rel="https://api.w.org/"
X-Varnish: 1812270 1794298
Age: 475
Via: 1.1 varnish-v4
Front-End-Https: on
Content-Encoding: gzip

For more info see Module ngx_http_gzip_module.