Safari's private mode keeps the browser from saving the pages you visit, the searches you run and the information you enter in its history. You can freely switch back and forth between private and normal browsing without losing the pages you have opened; in fact, any pages you open while in private mode remain open until you close them, even if you close Safari or switch your phone off and then back on.
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Tap the "Tabs" button on Safari's toolbar to bring up the tab switcher. If the toolbar is not currently visible, tap once on the address bar to display it.
Tap "Private" to switch Safari to private mode.
Tap either the "Plus" button or "Done" to open a blank tab and start browsing. If you've used private mode before and you left pages open, tapping the "Plus" button opens a blank tab, while tapping "Done" returns you to the last tab you had open; you can also tap any of the tabs in the tab switcher to open it.