First, make sure your browser isn't storing too much about you.
In the settings menu, turn off the ability for the browser to store the passwords you use to access websites and services.
That can be a pain, as you should have a different password on every service you use, so an alternative is to use a password manager, like PCMag's five-star Editors' Choice, LastPass.
Browsers also store things like images, surfing history, and what you've downloaded, as well as cookie files, which can remember helpful things like settings and passwords.
Obliterate that info occasionally—in Chrome, IE, and Firefox, you can type Ctrl+Shift+Del to get a pop-up that helps you get rid of them.
Use a product like CCleaner (Windows and MacOS) or SlimWare Utilities SlimCleaner (Windows only) to nuke these files for all the browsers you run.
Major browsers also have anonymous surfing modes.
In Google Chrome it's called Incognito (Ctrl+Shift+N to access); in Firefox it's Private Browsing and in Internet Explorer it's InPrivate browsing (Ctrl+Shift+P for the latter two).
That will prevent the browser from saving info on pages visited, whatever you search for, passwords, cookies, downloads, and cached content like images.
There are also a number of browsers that bill themselves as privacy-focused. Of course, they all use the same rendering engines as the big names, especially Google's Chromium engine, but the difference is the browsers don't share any info with Google.
Examples include Comodo Dragon, Comodo IceDragon (based on Firefox), and Dooble.
You should also start using a different search engine than Google, Bing, or Yahoo, all of whom want to sell, sell, sell you.
Instead, try DuckDuckGo, a search engine that doesn't track you or sell your info, they promise.
Keep in mind, using stealth modes and special browsers don't make you completely anonymous on the Web, but they do prevent sites from writing info to your computer, including cookies, which can later be read by other sites to figure out your browsing habits.