I recommend you to back up your PS4 games and other data to external hard drive first. That way we can restore all the games and saved data without having to download everything again (which can take a really long time depending on your Internet speed). Follow the instructions on this page:
http://manuals.playstation.net/document/en/ps4/settings/backup.html
After the backup process is done, you have to download the latest PS4 firmware. Make sure that you download the whole firmware file (approximately 900MB for v3.11) and not just the update file (~250MB). Scroll the page to the section: Perform a New Installation of the System Software. There should be a download link there. Here is the URL to the firmware page:
https://www.playstation.com/en-us/support/system-updates/ps4/
Now, the last step is to replace your PS4 HDD, reinstall the firmware, and restore the backup. Follow the instructions on this page:
https://support.us.playstation.com/articles/en_US/KC_Article/Upgrade-PS4-HDD/