I am a new Nginx web server user. How do I redirect to a different domain using nginx (say example.org to example.com) permanently?

You need to use HttpRewriteModule module to change URI using regular expressions (PCRE), and to redirect and select configuration depending on variables.

rewrite directive

This directive changes URI in accordance with the regular expression and the replacement string. Directives are carried out in order of appearance in the configuration file. You can use this directive in the following context:

• server
• if
• location

Nginx 301 rewrite syntax

The syntax is:

rewrite regex replacement [ flag ]

Flags can be any of the following:

1. last – completes processing of current rewrite directives and restarts the process (including rewriting) with a search for a match on the URI from all available locations.
2. break – completes processing of current rewrite directives and non-rewrite processing continues within the current location block only.
3. redirect – returns temporary redirect with code 302; it is used if the substituting line begins with http://
4. permanent – returns permanent redirect with code 301

Example: Redirect to a different domain with nginx

In this example, redirect all traffic as follows:

From:	To:
example.org	example.com
example.org/foo.html	example.com/foo.html
example.org/show.php?arg=value	example.com/show.php?arg=value
example.org/dir1/dir2/bar.cgi	example.com//dir1/dir2/bar.cgi

Edit nginx.conf or your virtual host config and update server context as follows:

server {
  server_name .example.org;
  rewrite ^ http://example.com$request_uri? permanent;
  # rest of config, if any goes below ... #
}

Finally, restart/reload your nginx server, type:
# nginx -t && nginx -s reload

How do I test and verify HTTP 301 redirect?

You need to use curl command:
$ curl -I http://example.org/
$ curl -I http://example.org/foo/bar.html
Sample outputs:

HTTP/1.1 301 Moved Permanently
Server: nginx
Date: Mon, 18 Nov 2013 12:29:08 GMT
Connection: keep-alive
Keep-Alive: timeout=60
Location: http://example.com/foo/bar.html
Vary: Accept-Encoding
X-Galaxy: Andromeda-2