How do I bypass firewalls???

Its getting very difficult for these things to work. The updates to the filtering settings generally find them quickly so even if you find a new one that is allowed through, it probably wont be for long (depending on what is actually doing the Internet Filtering)

How exactly such updates work? Can it be done automatically? Or person who is responsible for maintaining network has to let say once a week download new list of black ips?

It all depends on the software being used, generally its much simpler to purchase software to do this otherwise its a massive task. Websense for example update their database every other day.