As the title suggests, How can I become anonymous over the internet, i.e disallow the websites from tracking my public as well as private IP address. Please help!
You have many many options to varying degrees of anonymity. One of the best options is to use TOR browser and connect to TOR network and follow all the guidelines provided by the TOR community.
Simpler steps include, using the incognito or private browsing mode in modern browsers and using anonymous proxy servers