There are some browsers that don't track user information (or do so only minimally). These free add-on apps work on top of Google Chrome:
The free Brave add-on works with either Chrome or Safari. The Electronic Frontier Foundation's Privacy Badger currently works on top of Firefox, Firefox for Android, and Opera.
Virtual Private Networks (VPNs) claim not to store any information about you. This 2017 article from Wired gives more details:
Make sure that your browser's settings reflect your privacy preferences. You can do this by setting security parameters in your browsers. Pay attention to:
and use an Ad-blocker, if possible
CalTech offers comprehensive advice on what to turn off for improved privacy. WikiHow gives directions for Internet Explorer, Mozilla Firefox, and Apple Safari; and Consumer Reports has an article on Google Chrome privacy settings.
Some browsers offer a "private" or "incognito" search mode (available in Mozilla Firefox, Google Chrome, Apple Safari, Microsoft Internet Explorer).
Using the web in this mode will interfere with some functions that require identity tokens (filling in forms, using pop-ups or cookies, etc,) - you might decide that is a fair trade-off. The University of Michigan has posted quick links to private browsing here, and the National Network to End Domestic Violence's Technology Tips has more details.
Check your privacy security - test for webtracking with Electronic Frontier Foundations' Panopticlick tool.