Start by doing a lot of digging. There is very little known about the actual practices performed in ancient Greece. There are a few modern pagan groups running around though that use the ancient Greek as inspiration.
As far as conversion: Simply start by making a declaration of allegiance to the Gods and Goddesses and then begin practicing based on what you were able to learn from your research.
Greco Paganism
Their religion was what we call the Greek myths., Today, it would probably be referred to as "Paganism".
It's known as Norse paganism.
Norse paganism.
He managed to convert much of Ireland from paganism to Catholicism.
Some aspects of ancient Greek and Roman paganism are reflected in the Catholic faith, particularly in its system of patron saints. The clothing used by Church hierarchy is said to be based on those used by officials in the Roman empire.
The origins of Christianity are clearly in the early Jewish faith. Some see further influences from Greek paganism and ancient Greek philosophy, particularly Platonism. Others say that Christianity could have evolved from the mystery religions.
Ancient Greek
Paganism is not a single, organized religion with a clear founder or founding date. It encompasses a diverse set of beliefs and practices that predate organized religions like Christianity and Islam. Paganism has ancient roots in various cultures and regions around the world.
It was mostly Hinduism and various forms of Paganism.
The origins of Christianity are clearly in the early Jewish faith. Some see further influences from Greek paganism and ancient Greek philosophy, particularly Platonism. Others say that Christianity could have evolved from the mystery religions.
An Ancient Greek is a native or inhabitant of Ancient Greece, the Greek-speaking world of ancient times.