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 Contacts, then tap Fix & manage located at the bottom right corner of the screen.
2. Tap Export to file. Select the location where to save the contacts and 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.