Special Domains FAQ -- "For registering Top Level Domains that are not .com, .org or .net"

... what are the guidelines for registering an .EDU Domain name?

... The .EDU TLD is reserved for 4-year-degree granting (accredited) colleges and universities. Each college or university may register only one .EDU Domain name. Graduate programs, remote campuses, etc., cannot obtain an .EDU Domain name of their own. Instead, they should obtain a third-level Domain beneath the second-level Domain of their institution. Inquiries should be directed to the registrant of the second-level Domain.

If the college or university registering the Domain name meets this criteria, it must provide a brief explanation of the kinds of degrees awarded under "Purpose/Description" on the registration form when registering the Domain name with the registrar.

Alternately, many foundations, institutions, consortia, centers, etc., with educational missions but not meeting the criteria for a Domain name in the .EDU TLD, register their Domain names under the .ORG TLD. K-12 schools and community colleges are typically registered under country Domains such as .US.

... what is this .CC Domain extension I keep seeing?

... The .CC extension is simply another method to address locations on the Internet.

.CC works just like .COM. Both are called top level domains, or TLDs. .COM and .EDU are examples of generic domains. Other examples are .NET and .ORG. To allow room for growth, the designers of the Domain Name System also created country code domains assigned to particular places in the world. The "CC" refers to a tiny island chain in the Indian Ocean. The extension .CC is technically a designation for the Cocos (Keeling) Islands, a territory of Australia located in the Indian Ocean with fewer than 700 residents. eNIC Corporation acts as the administrator for this top level county code.

... how do I register a Domain name in the .GOV, .CA, ... or a country specific TLD?

... That is a BIG question, we don't have room on this page to answer it specifically, so Host2Host has put together a listing of some (US / Stateside) Domain name registration authorities, provided a list of the TLDs they support and (when available) coded direct links to their main URLs, FAQs, Help Sections and Domain availability search page.
Note: The following registration authorities are in no particular order or listing hierarchy.

Main URL; http://www.nic.gov/ -- Government-Wide Registration Service
TLDs supported; .gov
Domain name availability search page; http://www.nic.gov/ click on I consent to monitoring
FAQ/HELP; http://www.nic.gov/REFERENCE/

Main URL; http://www.nic.mil/ -- Department of Defense Network Information Center
TLDs supported; .mil
Domain name availability search page; http://www.nic.mil/cgi-bin/whois
FAQ/HELP; http://www.nic.mil/LIBRARY/whatisit.html

Main URL; http://www.ina.com.au/ -- Internet Names Australia
TLDs supported; .com, .org, .net, .com.au, gov.au, edu.au, asn.au info.au org.au, net.au, oz.au, id.au and conf.au
Domain name availability search page; http://www.ina.com.au/services/servicesfr.html
FAQ/HELP; http://www.ina.com.au/help/helpfr.html

Main URL; http://www.oleane.com/ -- France Télécom -- Pages are written in French ...
use AltaVista Translations at http://babelfish.altavista.digital.com/cgi-bin/translate? to convert from French to English or ...
load the English Version at http://www.oleane.com/english/ There is limited information on the English site with regards to France Télécom being a registrar of Domains.
TLDs supported; .com, .net, .org and ??????
Domain name availability search page; ??????
FAQ/HELP; ??????

Further Reading

http://www.isi.edu/div7/int/ -- Information Regarding the .inf Domain

http://www.iana.org/ -- The Internet Assigned Numbers Authority

http://www.icann.org/ -- The Internet Corporation for Assigned Names and Numbers

http://www.din.de/gremien/nas/nabd/iso3166ma/index.html -- ISO 3166 Maintenance Agency (ISO 3166/MA)

http://www.gTLD-MoU.org/ -- Generic Top Level Domain Memorandum of Understanding

http://www.iana.org/cctld.html -- Country Code WHOIS Contact Information is provided by the Internet Assigned Numbers Authority at http://iana.org/