How do I save all the stored information on my iPhone 4? I need to do a factory reset to my iPhone 4, but don't know how to save my stored information such as my Contacts, Pictures, and Purchased apps.
Apple makes backing up iOS devices easy. Just make a backup of it with iTunes or iCloud, as detailed in this Apple guide.

For Photos, just use the Photos app to import them all to your Mac. If you're using a Windows machine, open My Computer, double-click whatever represents your iPhone and copy the folder marked "DCIM" to your computer.