How do I restore my contacts from iCloud?

If you had previously synced your contacts to iCloud go to Settings/{your name}/iCloud and turn on the switch for Contacts. You can see if your contacts are in iCloud by going to https://icloud.com and clicking on Contacts.

If you did not sync your contacts, but did back them up to iCloud, you must restore the iCloud backup to your phone. See this Apple support article-->Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

If I haven't guessed correctly what you are trying to do please enlighten me.