How to Do Private Browsing in Mozilla Firefox Open Mozilla firefox browser on your Computer. Press “Ctrl+Shift+P” on your Keyboard. A New window appears and confirms you that mozilla firefox is in private browsing mode. In a Private Browsing window, Firefox won’t keep any browser history, search history, download history, web form history, cookies, or temporary internet files. To stop Private Browsing, you can close this window and start using the firefox as you normally do. This is How You can do Private Browsing in Mozilla Firefox.