Open up the bright orange Firefox menu in the top-left corner of your browser window. Click "Start Private Browsing."

If this is the first time you've used Private Browsing, you'll get the following message. Go ahead and check that box to avoid getting the same message every time.

Once you've got Private Browsing active, the orange Firefox button will turn purple, and the address bar will be marked with an icon of a mask.

To stop Private Browsing, go back to the Firefox menu and click "Stop Private Browsing". Your non-private tabs will appear right where you left them.

Now, if you've currently got the Menu Bar active within your Toolbar settings, you won't see an orange button in the top-left corner. Instead, you'll find the "Start Private Browsing" option within the Tools menu. Everything else will work exactly the same way.
Open up the Settings menu. It's the little wrench-shaped icon in the top-right corner. Click "New incognito window." That's right. You're about to go incognito.

Chrome will open up a separate window for your private browsing needs. Your original window will remain in the background. Appropriately enough, Incognito mode is marked with a little fedora-clad gumshoe.

To return to normal browsing, just close the Incognito window.
See that little gear in the top-right corner? Click it.

Next, mouse-over the Safety menu. Click "InPrivate Browsing."

Like Chrome, IE9 will open a new browser window, leaving your open tabs intact. You'll know the InPrivate browsing window by the dark blue "InPrivate" icon to the left of the address bar.

Close the InPrivate window whenever you're ready to stop being careful.