Before get started, it is necessary to make sure you have backed up your information on device to iCloud. Go to Settings> iCloud > Storage > Manage Storage to check the backed up files. If you have not done it yet, back up data to iCloud first.
After a series of setting to a new device, you will enter the following interface. Tap "Set up your iPhone". Select "Restore from iCloud Backup" and then sign in your iCloud account. After proceeding "Choose backup", you can transfer data from the list of available backups in iCloud to your new iPhone.
Note: To make sure the process go on smoothly, you should have you iPhone plugged in to a power outlet and connected to a reliable Wi-Fi network.
With the process above, your data on the old phone is easily transferred to your new iPhone. In terms of changing another device, here is a tip for you: To keep your personal information save, you'd better erase your old iPhone data if you want to sell or discard it.