The best method of hiding your IP address is to use a proxy server in some form.
It can either be a direct proxy that will mediate your connection requests and which can be set into the browser that you are using; or the method of using an anonymizer web service.
The manner in which this would work is that you would first connect to the website that provides such services. Then on the webpage, there would be an option of entering a URL: for this, you would want to browse anonymously.
Once the URL is entered, the website will make a connection to the end server without revealing your identity. So, in effect, you would have hidden your IP address from the end server (e.g., Proxify.com).
Anonymizer services are also available on the internet to allow users to hide their actual IP addresses. You can use these anonymizer services by installing a small piece of software called anonymizer software.
A few examples of such software are:
VPN services are also available across the internet, which would allow you to channel your traffic to the VPN server, and then the VPN server would act as an intermediary for your traffic.
Examples of such services are: