How do I update iOS 6.1.3
How do update my IPhone with iOS 6.1.3
iPhone 4, iOS 6.1.3
If your iDevice is using a version of iOS lower than 5, you will need to use iTunes on your syncing computer to perform the upgrade. Use the Apple link below as a guide for the upgrade.
http://support.apple.com/kb/HT4972
Also read the instructions from the section entitled "Update your device using iTunes" at the link below.
http://support.apple.com/kb/HT4623
Information regarding transferring purchases from your iDevice to iTunes on your syncing computer can be found at the link below.