This is how I have done from upgrading a Jailbroken iOS 5.1.1 to new iOS 7.0.4.
With a 4s with 32GB, it took me 4 hours for the whole process. Good luck!
1. Must use iTunes to do a full iOS upgrade. OTA (wifi) will cause system error.
2. All JB apps and function will be deleted after iOS upgraded.
3. iPhone, goto: Settings > iCloud > Backup & Restore > Backup now!
4. Update to latest iTunes on your computer.
iTunes, goto: File > Devices > Transfer Purchases
6. Check your computer’s backup copy dates. Make sure it is today’s date, otherwise, make a backup now!
iTunes, goto: iTunes > Preferences > Settings.
7. Check your iCloud backup dates also.
8. iTunes, click: “Restore”, not Update!
9. If you see the following error message:
Error 3194 or “This device isn’t eligible for the requested build”
Mac, open: Terminal, then do the following:
a) change root user
$ su –
b) Comment out gs.apple.com
# vim /private/etc/hosts
Redo step 8.
10. Do not unlock screen! after upgrade to iOS7, choose to restore from latest backup via iTunes.
11. Make sure backup restoration is completed 100%. If found out missing apps, please manually install them back. App data should be retained.
12. If App Data get lost, then repeat step 8, after upgraded iOS, then unplug cable, choose iCloud restore from iPhone setting.
a. If you need to downgrade, use TinyUmbrella, http://blog.firmwareumbrella.com/
b.Old firmwares download site:
iOS 6: http://www.newmobilelife.com/2013/01/29/ios6-1-download-firmware-directlink/
iOS 5: http://www.ijailbreak.com/news/download-ios-5-1-1-firmware-apple/
c. Other’s blog: http://www.wretch.cc/blog/bitegame/16546402