If you would like to equip yourself with the tools to browse the internet without being traced or blocked, you have a couple of options, but by far the best option is to get a VPN service.
There are many VPN services out there, so be sure to shop around and read their terms and conditions to understand what you are paying for.
So how does VPN work? Well, first you need to have some basic concepts down regarding how networking works - see Networking 101 - Basic Terms Explained if you grasp all of the concepts regarding that article, then the rest of this explanation will make sense.
A VPN is a Virtual Private Network, in other words, you are connected on a private IP to somewhere else and due to the fact that your traffic through that VPN is encrypted, it is very difficult to decipher what is being sent/received through that encrypted tunnel. Taking the analogy of a building with many phone extensions, imagine that your cell phone was dialing through a switchboard at an office building so that your calls looked as if you were dialing from that building. If anyone were to trace your call, it would lead them back to the building, but no further, if that makes sense.
So, for instance, if you are using a VPN service like VPNtunnel.se your connections would trace back to servers in Sweden and no further. This would give you anonymity.
By the way, this is a great way to check your personal e-mail or order those shoes from your office without anyone knowing what you are doing. If you use wifi access at a free wifi hotspot, the use a VPN is highly suggested so that you can maintain your privacy. Should someone at that wifi hotspot filter traffic through a proxy server, they could intercept all kinds of personal data if you fail to secure your connection via VPN.
Just like anything else, something built for safety and security can be misused for other purposes. It is the responsibility of the user to take this information and use it in accordance to the laws that are applicable in their respective country and/or state.
Many companies around the world employ their own VPN in order to provide their employees a safe portal to their internal network resources.
There is a lot more to discuss in regards to this subject, but this will get you started.