Dawn,
The Greek property tax is called ENFIA and is payable in 5 monthly installments, or all in one go, usually starting in September and ending in January. The amount you pay is based on the size of the property and the size of the land. Your accountant will be able to tell you how much the tax is and will give you a payment code so you can pay it via internet banking.
If the property you are buying is pre-owned, the vendors should be able to provide details of the property tax they paid. That should give you a steer to what you will pay.