You can back up your contacts to your phone's internal storage or Google account.
To back up contacts to internal storage:
1. Go to Settings, select your Account at the top right and tap Contacts app settings.
2. Under Manage contacts tap Export and select the location where to save the contacts. Tap SAVE.
To back up contacts to your Google account:
1. Go to Settings, select Accounts. Ensure you are logged into your Google account, otherwise select add account.
2. Tap your Google account and then select Account sync. Enable Contacts and these will sync to your account.