How to browse Anonymously

There are many ways to browse the internet anonymously or to hide your IP Address
But first why go anonymous at all:

1. Hide their identity
2. Avoid leaving a digital footprint
3. Prevent Web tracking
4. Hide their geographical location
5. Bypass any bans or blacklisting of their IP address

 These are only the basic reasons not every reason is listed and those listed are the most common or more accurately the most common reasons listed by users in a online survey

How to actually browse anonymously or with your IP address hidden

Using a Virtual Private Network (VPN)

A virtual private network (VPN) extends a private network across a public network, such as the Internet. It enables users to send and receive data across shared or public networks as if their computing devices were directly connected to the private network. Basically when you go online, you'll be showing the world a different IP address...one that's on loan from the service you're using. Using service like:

VPN Unlimited
Open VPN
Hide My Ass
Spot flux
Hotspot Shield

VPNs can be free or you can pay for the service. They help you get on the Internet and assign you a different IP address, but there's a wide range of reliability in providers.

 

 

Using a TOR browser  

TOR is a free software that prevents people from learning your location or browsing habits by letting you communicate anonymously on the Internet.

The Tor Browser is a version of Mozilla Firefox that has been modified by the Tor Project for enhanced security and privacy. When you open the browser, it automatically connects to the Tor network, which encrypts and bounces your connection to the Internet around in a way that's supposed to make it difficult to spy on you.. Tor protects you against a common form of Internet surveillance known as "traffic analysis." Traffic analysis can be used to infer who is talking to whom over a public network. Knowing the source and destination of your Internet traffic allows others to track your behavior and interests. This can impact your checkbook if, for example, an e-commerce site uses price discrimination based on your country or institution of origin. These is the link used to download the TOR Browser or through these secondary link Tor Browser

Through Proxies

Proxies, also known as proxy servers, are great ways to surf the web anonymously, if that is what you are hoping to do. These are basically routing machines that act upon your requests to forward any data of yours. This helps you completely stay away from any direct communication where data is typically handled and taken care of. These anonymous proxy websites are not necessarily said to be the best option because they are not one hundred percent secure.  It is, however, safer than simply browsing online without any protection or security, so it is a good option for some level of protection.
There are many proxy services available these are not the only ones 
Hideme
Public Proxy