To use Chrome’s private browsing mode, click on the File menu and select New Incognito Window. Sites visited while using the Incognito Window are not saved to the history.
From the Tools menu, select Delete Private Data. You can then just click the Delete button. Or, you can click the triangle next to Detailed Options. That will show you a laundry list of things you can delete. The default choices are a good selection, but you can make changes if you want, then click Delete.
In Opera’s preferences (Opera -> Preferences), click on History in the left column. Here, you can also clear the history and cache, and well as adjust settings.
In the File menu, Opera has options for New Private Tab and New Private Window. If you use these, the history is automatically deleted when you close the tab/window.
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