In Chrome:
Click on the 3 dot menu on the top right, then select New incognito window. You can also use the associated keyboard shortcut: Ctrl+Shift+N
In Firefox:
Click on the 3 line menu button and select New Private Window. You can also use the associated keyboard shortcut: Ctrl+Shift+P
In Safari:
Click on File and select New Private window. You can also use the associated keyboard shortcut: Shift+Command+N