If you want to attain Edward Snowden and Laurie Poitras levels of online security and privacy, a good place to start is with Tails, an open-source, Linux-based operating system that's designed to reduce the chances you're being spied on.
The idea behind Tails is to bypass the Mac or Windows operating system you use on a regular basis and boot straight to a USB drive that contains an open, vetted, and privacy-tuned system and set of applications.
While you can never be assured of perfect security, running Tails wipes out most of the known security vulnerabilities that are commonly found in commercial software.
Tails also locks down the operating system to favor privacy settings over all else, such as with the bundled web browser, Tor, which allows you to browse the web anonymously.
When you're done being more secure than usual, you can reboot back to your regular Mac or Windows system to continue using your computer normally.
Check out the Tails website to learn more about it and download it for free.