First is honoring the gods of Greece and Rome. For most of us, that means the twelve or thirteen deities who are said to dwell on Olympus. This is pretty straightforward. I’m not sure I believe in resurrecting every last ancient festival to whatever deity. But we know more or less the rites and the mindsets by which the ancients honored their deities, and with some adaptations we can bring this into the modern era. In particular, I think the Roman idea of daily devotions at a household altar (lararium) is especially suited for modern worship.
Second is honoring our ancestors and the local spirits. Both religions have their rites and festivals for doing this. Some people may be disinclined to honor their biological ancestors for whatever reason; in such instances I feel it is very easy to make the case that the ancestors most relevant to our religions are our cultural ancestors, the Greeks and the Romans. We honor them by eagerly studying their ways, internalizing the best of their traditions, and keeping their legacy alive in the modern world. Also, citizens of mega-cities may find it difficult to honor land spirits in any meaningful ways. In such cases, a broad concern for environmental issues can possibly take the place of more focused worship.
Third is a concern for our rights and responsibilities as citizens. Most of our broader ideals on government and citizenship come to us from our Greco-Roman ancestors, and we honor them by emulating their ways. There would be a mistake in thinking Greek and Roman paganism demand membership in a particular political movement or party. Rather, Greek and Roman paganism merely imply a commitment to active, responsible citizenship in whatever manner that may take.
Fourth is an acknowledgement of cosmopolitan societies where “race” and “tribe” are less important than culture and government. It’s very true that the Romans and Greeks could be rather contemptuous of outsiders. It’s also very true that their cultures were spread and adopted - often by outsiders! - beyond the original ethnic borders. In modern terms I believe this means viewing matters through the prism of culture before the prism of ethnicity. There might be times to take exception to other cultures and other ways of life, but ethnicity per se shouldn’t be a factor in such instances. Ideas count more than blood, especially if they are Greco-Roman ideas.
Fifth is understanding our ancestors’ views on human sexuality. While those sultry Mediterraneans have a reputation for orgies, in reality moderation and self-restraint were the stated ideals. Furthermore, our ancestors didn’t have quite the same views on same-sex relations that some cultures and religions do. Also, it must be noted, prostitution in some cases was perfectly legal. Charges of pedophilia are somewhat overstated as Greek men took post-pubescent males for their companions, rather than the pre-pubescent children that are the main victims of pedophiles.
Sixth, reason and intellectualism are part of the Greco-Roman legacy. Both Greeks and Romans could be downright superstitious at times, far from bastions of logic. Nonetheless, there was an area for intellectualism and critical thought that may be absent in other traditions. While that intellectualism did at times take pot shots at the religions we are trying to reconstruct, we nonetheless can claim it as our own. In the broadest sense it means that science, philosophy, and the arts are critical human endeavors.
Seventh is competition, the pursuit of excellence, and one’s proper standing in the community. These three concepts are all linked. Other religions may prize humility and subservience - ours don’t. Honor and glory were important to our ancestors. They were always in competition with each for it. To be the best athlete, the most eloquent poet, the most victorious general, the craftiest statesmen – this is what concerns the great. Life is a pursuit of excellence, garnered from competition, ranking one’s place in society. Just remember there are some limits to it. Hubris, or overweening pride, can lead to downfall. Know your limits, and moderate your ambition accordingly.
Eight is hospitality. This is pretty straightforward. Be generous to friends and family and allies. Don’t be overly frugal in entertaining strangers. Extend hospitality to others in the belief you might require it yourself someday.
Ninth is moderation, of knowing what limits to not transcend. If we are to believe the oracle at Delphi, this bit of advice comes from the god Apollo himself. Our ancestors didn’t always live up to their ideals of moderation – and they usually paid for it (witness the corruption and excess of later Rome). In general, though, moderation and self-restraint were the watchwords of Greco-Roman civilization. For the good of the individual and of the community, there must be temperance in all things.
Finally, what ties everything together is a pious respect for the past, a concern for the ways and wisdom of our ancestors. Our ancestors themselves seemed to be generally conservative – that is, not desiring excessive change for its own sake. Not everything our ancestors did is practical or desirable to resurrect for the modern world. Nonetheless, we ignore our ancestors at our own peril. By studying their triumphs and their failures, we better understand who we are. By living up to the better parts of their legacy, we can find honor and meaning in our own lives.