While there are many proxy server solutions to remain anonymous, currently the best and easiest way to mask your ip is through onion routing, using tor. The basic idea behind onion routing is that your connection will go through a series of tor routers that only know who the connection is from and where they need to make the next connection. This means that your connection will go through a series of other servers that together mask your IP address.
You can download the latest tor bundle for your operating system at:
Draw Backs of Anonymous Browsing
The first is that when you make google searches, they will ask you for human confirmation, this is really easy, you will just have to enter a captcha.
The second drawback that while you are browsing anonymously it is strongly recommended that you do not use any plug-ins. This includes flash. This is because there could be a tor router that could inject a new executable that your machine would run. To bypass this you can disable tor when watching flash videos.
The third drawback is the speed. It will take longed to send and receive data because you are going through so many different connections.
Anonymous browsing is not encrypted browsing. There is a big difference between anonymous browsing and encrypted browsing. encrypted, and signed data can be transmit through the tor network but just because you are using tor to mask your IP does not mean you are secure.