Buying Iphone

1. Make sure it has been properly erased, and is ready for you to set up. If its not sitting at the "Hello" screen, it has not been properly erased. Steps that should have been followed by the seller or previous owner: What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support
2. Make sure the iCloud account it was logged into has been signed out, and Find My iPhone has been turned off. Otherwise you will encounter activation lock, and the iPhone will be useless to you. If item 1 was completed correctly this item will have also been correctly turned off. More info here:: Turn off Activation Lock - Apple Support
3. Make sure it is unlocked for use with other carriers, otherwise unless you use the same carrier as the person selling it, you will not be able to get cellular service on it with your carrier. Previous owner would need to contact their carrier to have them unlock it. Apple does not unlock iPhones for use with other carriers. Only the carrier it is locked to can unlock it. Only the previous owner will be able to request the unlock from their carrier as most require the requester to be a current customer in good standing. See here: How to unlock your iPhone for use with a different carrier - Apple Support

Make absolutely certain that the previous owner has followed all the instructions in this link...

What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support