To open a Private Browser window in Safari, go up to the File Menu and select New Private Window. You can also use the Keyboard shortcut Shift + ⌘ + N.
Heads Up: Google calls their Private Browsing Mode "Incognito"
To open an Incognito Window in Chrome, open the Chrome Menu in the upper-right-hand corner of the browser window and select New Incognito Window. You can also use the shortcut Shift + ⌘ + N (on macOS), or Shift + CTRL + N (on Windows/Linux).
To open a Private Browser Window in Firefox, click on the Firefox Menu in the upper-right-hand corner of the browser and select New Private Window. You can also use the shortcut Shift + ⌘ + P (on macOS) or Shift + CTRL + P (on Windows/Linux).
Heads Up: Microsoft calls their Private Browsing Mode "InPrivate"
To open an InPrivate Window in Microsoft Edge, open the Edge Menu in the upper-right-hand corner of the browser window and select New InPrivate window. You can also use the shortcut Shift + CTRL + N.