How to create own domain extension?

You can run your own nameserver and add a new tld there. But this won't help you much, as the TLD will only be visible to the users who are using your own nameserver. The "official" TLD like ".ly" are countries, see: official list

You can't. Only IANA can.

Management of most top-level domains is delegated to responsible organizations by the Internet Corporation for Assigned Names and Numbers (ICANN), which operates the Internet Assigned Numbers Authority (IANA) and is in charge of maintaining the DNS root zone.

• http://en.wikipedia.org/wiki/Top-level_domain

Here's a list of available TLDs:

• http://www.iana.org/domains/root/db/
• http://data.iana.org/TLD/tlds-alpha-by-domain.txt