Google Chrome may be the most popular browser, but it does not have the best track record of respecting user privacy. The open source browser Firefox automatically includes a host of privacy enhancing tools, while also granting the user a degree of customizability. You can customize built-in privacy and security settings by clicking: Firefox -> Preferences -> Security and Privacy. Here, you will see settings for enhanced privacy protection. Additionally, users may install browser extensions to further customize privacy and security. See the right hand box on this libguide to learn more about these extensions. Or visit the Freedom of the Press foundation for an in-depth guide.
The Tor Project (The Onion Router) aims to advance human rights by combating surveillance and protecting privacy online. The Tor browser is built on the open source Firefox platform, but by routing traffic through a maze of relay nodes, it allows users to browse the internet without being tracked or monitored. Tor includes multiple layers of encryption, and resists fingerprinting and tracking. If you choose to use Tor, know that these benefits may be compromised if you log in to an account (for example, Google or Facebook) for the remainder of that session.
Tor is available on Android devices. On the iPhone, you can find Tor as "Onion Browser" in the App Store. Alternatively, Duck Duck Go can be used as either a default search engine, or as a browser itself. It is available on both platforms.