To clear your browsing history on Google or other search engines you'll need to go into the settings of your browser and find the security options and delete cookies and browsing history.
The settings differ depending on the browser you're using.
For Chrome you go to the top right corner of the browser and you'll notice three little lines.
Click on that icon and then a new page with options will open up where you can see security and settings and from there you'll notice a delete history and cookies option.