I am a practicing Hellenic pagan of many years. I also do other kinds of paganism which I might discuss on their own pages, but this is what I've done longest (going on 8 or 9 years at this point, which is still not that much compared to some people!).
What is Hellenic Paganism?
Hellenic Paganism, known also as Hellenic Polytheism (and more rarely Hellenismos, Dodekatheism, etc.) is the modern worship of Ancient Greek deities and following their beliefs and worldviews. You may note that I put beliefs and worldviews in plural: this is because Ancient Greece was a super large mass of land, so beliefs varied by era and place. The most common features are the worship of multiple gods in both private and civic settings, magic, giving offerings to make a request or give thanks, and animal sacrifice. While I do not personally practice animal sacrifice, I also do not condemn it either, as I am firmly of the belief that condemning animal sacrifice is a stance that marginalizes many other religions that are often misunderstood.
Reconstructionism vs. Revivalism
You may hear or see these terms around on the Net presented as a strict binary of "follows ancient practices exactly" or "do whatever who gives a shit". This is fundamentally an unhelpful framework for paganism at large and oversimplifies both ends. It's logistically impossible to be a reconstructionist without adjusting things to the modern era; conversely, you cannot make up your own thing and label it Hellenic Paganism or what have you. I believe that most people are in between these two labels.Inclusivity
Some people will tell you that paganism can only be practiced by a specific group. This is fundamentally untrue and is a white supremacist and racist argument regardless of the intentions of the person telling you this. Religions that require initiation, conversion, or ancestry are ones that did not need to be revived and are, therefore, inherently not pagan. Ancient Greece was a civilization that spread over multiple continents through centuries of conquest, and spanned to include modern Egypt, Bulgaria, Turkey, and more. Greece is not a country that is currently being oppressed in a racial or ethnic manner, and therefore any attempts to "safeguard" its ancient religion are inherently reactionary. Ancient Greek religions did not survive the arrival of Christianity, and anyone claiming to be secretly practicing a surviving form of it is lying to you. See the Xenia Declaration for more.