How do I tell if my contacts are backed up on iCloud?

It's not entirely clear whether contacts are included in your iCloud backup. They are synced to your iCloud account (which you can confirm by going to icloud.com on your computer and checking your contacts there), but don't count on your device backup to recover your contacts. If you want to be sure your contacts are backed up, use an app like My Contacts Backup, or sync them to a contacts management program on your computer that allows you to archive them for safekeeping.

The My Contacts Backup app does not back up your contacts to iCloud, it backs them up as a vCard (.vcf) file that is attached to the email. You can either save the email or save the .vcf attachment on your computer as your backup. If you ever need to recover your contacts, just open the email and tap the attachment and it will re-import them to your phone. (If you saved the attachment on your computer, just email it to yourself again as an attachment.)