Private Browsing masks your browsing trail from anyone who might later use that browser and try to check the browser's history, cookies, and other data to compromise your security and privacy. Using Private Browser and closing the browser when you are through also logs you out of web based applications you had been using. Shutting down the browser is insufficient, unless you are in Private Browsing mode. If you use Private Browsing mode, you don't need to worry about clearing your cookies and caches. Enable Private Browsing before beginning browsing.
Chrome, Menu Icon (Windows) or "File" Menu (Mac) -> New incognito window -> Look for private eye indicator in upper left hand corner. Official instructions from Google.
IE, Gear -> InPrivate Browsing -> Note “InPrivate” indicator in address bar. Official instructions from Microsoft.
Firefox, File -> New Private Window -> Look for “Private Browsing” notification in title bar. Official instructions from Mozilla.
Safari, Gear (Windows) or Safari (Mac) -> Private Browsing -> OK -> Look for “PRIVATE” indicator in address bar. Official instructions from Apple.