Depending on which OS X version you are using the means may vary.
The most recent OS X versions suggest these methods:
• Safari 9 (El Capitan): Clear your browsing history
• Safari 8 (Yosemite): Clear your browsing history
• Safari 6/7 (Mavericks): Delete your browsing history
support.apple.com/kb/PH17148?locale=en_US
Safari 6/7 (Mavericks): Safari shortcuts
Safari 9: "Clear history, not cookies"
How do I clear history, cache and cookies on Safari 8 +?
• Clear Search History - Safari:
https://duckduckgo.com/?q=Clear+search+history+in+Safari+&t=ffsb
Since I started this prior to other replies and checked each page,
hopefully this will be of use to someone, if not you. Also, if you
are using Mavericks 10.9.5 or before, you can also 'Reset Safari'
in the drop-down section of main Safari menu. Later version Do
Not have this reset. It does clear several items not just history.
There is a work around using History to clear these in later Safari.
Good luck & happy computing! 🙂