Use Tor

Tor, which stood for "The Onion Routing Project" was originally developed by the navy to aid in concelaing the identities of its users online. It accomplishes this by running a users internet traffic through the Tor network, eventually sending it out to the internet and then routing the response back through the network to the user. These constant reroutings are what provides the anonymity, as it is extemely dificult to track where the traffic travels within the network. Essentially, it protects you from the surveillance of your online activites by third parties. 

Usage case scenarios for this app includes needing to comunicate with others confidentially, avoid surveillance, or being just plain paranoid. Download it or find out more at the Tor website. They also have an android app to privatize your internet traffic while on the go. 

Keep in mind that like Tor, your security depends on having various layers for maximum effectiveness.