"Fah-eena" is what I would think would be the right way to pronounce it. If saying it quickly, it would sound a little like "Feye-na" ("feye" as in "eye")
It is pronounced: " Fi-ee-na " There is no letter "H" as in "-hee-" mentioned before, that would be wrong. They have troubled with the pronunciation of my name Faina all my life, Americans tend to say Fina as in Fine - which is also wrong, so I changed it to Faena, but they still can't get it right, sometimes they say Fiona.