How do I recover messages and contacts

If you were syncing Messages with iCloud and deleted them, they can't be recovered. If you weren't syncing Messages with iCloud, do you have a backup you can restore from? Restoring from a backup erases all data currently on your device. Any data newer than when the backup was made will be erased. A restore is an all or nothing restore. You can't access a backup and only restore certain files.

Backup - Restore your device from an iCloud or iTunes backup.    

For Contacts, if you weren't syncing with iCloud, restore from a backup. If syncing with iCloud,  try iCloud.com/Account Settings using a computer browser and go to Advanced at the bottom left. Access Restore Contacts.