What methods does the chinese gov. use to censor internet use by its
citizens? What methods do groups that want to get around this
censorship use?

Hi! Thanks for the question.

Based on my research, the most cited and considered authoritative
document about the methods of internet censorship in China is a study
by Jonathan Zittrain and Benjamin Edelman of Berkman Center for
Internet & Society at Harvard Law School done in late 2002. Up to now
this is the paper still cited by recent articles. Here is the link to
the paper:

"Empirical Analysis of Internet Filtering in China"
Jonathan Zittrain and Benjamin Edelman
Berkman Center for Internet & Society
Harvard Law School 
http://cyber.law.harvard.edu/filtering/china/ 

The details of the methods can be found on the technical appendix
attached to the paper. Please read the entire document to get a
detailed overview of the methods used. Here is a general list of the
methods employed.

- "Filtering on the basis of web server IP address."
- "Filtering on the basis of domain name server IP address"
- "DNS redirection"
- "Filtering on the basis of keywords in URL"
- "Filtering on the basis of keywords or phrases in HTML response"

"Technical Appendix Empirical Analysis of Internet Filtering in China"
http://cyber.law.harvard.edu/filtering/china/appendix-tech.html 


Our next article provides some of the methods use by people in China
to bypass such internet restrictions.

a.) The way the company does it is not new. It allows a user inside
China to access the internet, not through a system controlled by the
government, but through a proxy server.

"?The basic method of these technologies is to find a helpful computer
in the United States or Canada or Europe that is willing to act as an
intermediary for requests,? said Ben Edelman, a fellow at Harvard Law
School's Berkman Center for Internet and Society.?

b.) ?Others are taking more hi-tech approaches. They are developing
harder to crack encryption that would keep e-mails and proxy servers
secret.?

?Bypassing China's net firewall?
http://news.bbc.co.uk/2/hi/technology/3548035.stm 

 
Another article shows other methods and a more detailed discussion on
how to bypass internet censorship in countries like China.

a.) Use an ISP from another country
b.) ?Using a not censoring DNS-server?
c.) ?Using a non censoring proxy server?
d.) ?Using a Web-2-phone service?
e.) ?Using a webproxy?
f.) ?Get webpages via eMail?
g.) ?Using steganography?
h.) ?Using a special proxy like p2p program?
i.) Using Special Services like Usenet and Instant Messengers

The methods above are discussed in detail on the next link.

?HOWTO bypass Internet Censorship?
http://www.zensur.freerk.com/#4. 

 
Search terms used:
China internet censorship methods
China internet filtering software 2004

I hope these links would help you in your research. Before rating this
answer, please ask for a clarification if you have a question or if
you would need further information.
                 
Thanks for visiting us.                
                 
Regards,                 
Easterangel-ga                 
Google Answers Researcher

I hate communism, it just makes things hard for people, what, with all
the censorship and such, if the entire world were communists, we'd all
be cavemen, except for the government.

i think i might knw some basic answer to your problem.
Since all chinese ISPs are registered under the government regulation
policy, and all ISPs were ordered to be monitored by the chinese
police (digital criminal) department for the "secure" purpose.
1)All the website contained "forbidden" information (such as religion,
anti-government, etc) are already abandoned from the ISP's list. So,
you won't even be able to visit those sites at first place.
2)If there is new site/link has being accessed by someone in china,
the filtering software by the police department will filter out the
"sensitive" words, and check wether that site is dangerous and should
be abandoned.
3)to get around with that software is quite simple:
a) mirror as many sites/addresses as possible
b) send new site link through instant messenger software such as OICQ
c) use english rather than chinese, since that software was major
focused on the chinese contents.
there are many more ways to get through the ISP, but most often used
is still mirror sites. How chinese citizens get through that? google
search is definitely still the simplest way to find wat you want (open
the cached rather than original link)
hope my answers help you out a bit! hv fun!

Using the cached copy of websites through Google is one of the main
loopholes the chinese needed to fix in order to maintain censorship of
the Internet.

See the article: China Hijacks Google's Domain Name

Chinese government is not allowing some Web surfers to access the
popular search site.

http://www.pcworld.com/news/article/0,aid,104813,00.asp

You might want to read these articles in PC World about the Great
Firewall of China:

http://www.pcworld.com/news/article/0,aid,12833,00.asp

China Finds Freedom Behind Great Firewall
Country's first decade online has seen changes in restrictions, access.
Part 1: http://www.pcworld.com/news/article/0,aid,116278,00.asp