Below are the steps for purchasing the Premium from iTunes.
From the Contacts tab, press "Backup" or "Merge".
Press the "Buy" button on the bottom right.
You will be prompted to sign in again to iTunes.
Once signed in, you can press "Buy" to confirm the purchase or "Cancel" to cancel this request.
When the purchase is complete, you'll receive a confirmation notification.
*If you did not receive this notification, then the purchase did not go through and you won't have access to the Premium.
Now you can start exploring the features in the Premium. :)