How to Turn On History in Mozilla Firefox Browser? Open the Firefox Browser. Select the “Tools” Drop-down menu from the Top of the window. Select “Options” and choose “Privacy.” Click the “Firefox Will” drop-down box and select “Use custom settings for history.” Check the “Remember My Browsing and Download History” option. Also check the “Remember Search and Form History” option. Click “OK” to Save Your Settings. This is How You Can Turn On History in Mozilla Firefox.