It's pretty easy to back up your iPhone contacts, one of the easiest ways is using iCloud. On your iPhone, go to Settings - [Apple ID] - iCloud. There, scroll down and find Contacts, make sure it’s checked. Next, scroll down and find iCloud Backup. Tap on it and tick the option.From then on, every time you connect the iPhone to Wi-Fi, charge it, or lock it, iCloud will automatically back up the contacts and other selected data on your iPhone.