You can transfer all of your data and settings from your current iPhone running iOS 8 to a new one using either iCloud or iTunes 12. Both methods involve backing up your current iPhone and then loading this backup onto the new device. Both methods work equally well. Use the iCloud method if you don't have access to a computer.
Transferring Using iCloud
Connect the iPhone to a Wi-Fi connection.
Touch the "Settings" icon on the Home screen to open the Settings app.
Touch "iCloud." If this is the first time you've used iCloud, you may need to sign in using your Apple ID.
Select "Backup" or "Storage & Backup" on the iCloud screen and toggle the "iCloud Backup" switch to the On position.
Touch "Back Up Now" to back up the iPhone to your iCloud account. This may take several minutes.
Turn on your new iPhone to initialize the Setup Assistant. Follow the prompts to choose your language and country, enable location services and join a local Wi-Fi network.
Touch "Restore from iCloud Backup" on the Set Up iPhone screen, select the backup you created on your old iPhone and touch "Restore." [refs 1, 2]
Transferring Using iTunes
Connect the iPhone to your computer via USB or Wi-Fi and launch iTunes 12 on the computer.
Select your iPhone on the list of available devices in iTunes, click the "Summary" tab and click the "This Computer" radio button under the Automatically Back Up heading.
Click the "Back Up Now" button to back up your iPhone's contents onto your computer. This may take some time depending on how much data is stored on the iPhone.
Turn on the new iPhone to initialize the Setup Assistant.
Follow the prompts until you reach the Set Up iPhone screen and then touch "Restore from iTunes Backup."
Connect the new iPhone to your computer and open iTunes. Make sure you use the same computer you used when backing up your old iPhone.
Select "Restore From Backup," select your backup on the provided list and click "Continue." After the backup is loaded onto the new iPhone, use iTunes to sync any additional music, apps and other content onto the device. [refs 1, 2]
If you’re planning to give away or sell your old iPhone, take a moment to prepare the device before doing so. After backing up your data and other content, open the Settings app, select “iCloud” and tap “Sign Out.” Tap “Sign Out” again and then touch “Delete From My iPhone.” Enter your password to confirm you want to disassociate your iCloud account from the device. Return to the main Settings screen, touch “General,” select “Reset” and then tap “Erase All Content and Settings.”
If you perform the transfer using iCloud, you can then connect the new iPhone to your computer in order to sync additional music, apps and other content onto it using iTunes.
If your old iPhone has a SIM card you plan to use on your new iPhone, remove the SIM card using a paper clip or SIM-extractor tool. Insert the paper clip or SIM-extractor tool into the small hole on the side of the iPhone.