How can I get contacts from one email account to sync to another email account?
I don't think this feature exist. It's not hard yet not trival to know the sync direction: from google to yahoo or vice versa.
For me using the built in import / saving to CSV (good backup) is the easy choise, (It does not keep my contact updated).
I thing that for ongoing sync someone will have to create an app and even then you will need to run it manually.
You don't, as you basically do not need to: all contact information from all connected accounts are shown in the single People Hub on your phone.
If you have a specific use case where you need to move/migrate/sync contact information between different accounts or account types, you will need to look to a third party software solution that will enable you to do this.