Something that may be new to someone starting out in a number of polytheistic religions is the idea of oaths.
In the broader culture, oaths are significant in part for their rarity–if you marry, the ceremony will likely include an oath, and if you are called on to appear in court you will swear one, as you will if you take on a public (or, sometimes, a private) office. It is kind of a big deal, not least because most of us will only do it on occasion, if ever.
In ancient Greece, though, oaths were a commoner occurance. There was even a god, Horkos, whose main calling was the swearing of oaths. And the breaking of oaths was a severe enough offense that Zeus himself would exercise his wrath against the oathbreaker. In other words, for the ancients, oaths were definitely a significant matter. The Delphic maxims warned against the swearing of oaths (“19. Do not use an oath”), but for anyone active in public life that was easier said than done.
Personally, I have not sworn many oaths. I swore a marriage oath. I swore an oath to Aphrodite. But I am, I will admit, a little oath-shy.
Something I’ve observed in the heathen community is a certain amount of less-than-functional oathing. (I’m not saying it’s unique to heathenry, just that it’s a comparatively larger community with a longer history than most modern polytheistic faiths, which means that custom has had a longer time to develop and solidify, and that there’s just been more opportunity for things, good or bad, to happen.) I think this may have to do with the role played by oaths in our broader culture, where they are sworn only rarely–we are not accustomed to them. So, say that an oath is sworn, perhaps for an important matter, perhaps not. Say, too, that the oath is broken. The fact that an oath was broken adds significantly to the bad feeling that results–not only did the person do whatever it is they did, they also broke their oath. Friendships are ended that might otherwise be repaired, because even if the offence itself might be forgivable, the broken oath is not.
I am not saying here that a broken oath is not a significant thing. I am saying that the oath itself is also a significant thing and should not be sworn frivolously or without great care.
And the ancients, I think, thought the same. An oath sworn in ancient Greece would generally take a fairly specific form–it would usually be sworn in the name of a god or gods, and it would specify what penalty would be suffered by the oath-taker should they fail to keep their oath.
Any oath was of course significant, but there were a few ways the ancients could mark the importance and sacredness of a particular oath.
Going to a holy place, a temple of sacred grove, to make an oath would grant it some additional weight. (Similarly in modern heathenry an oath sworn during sumbel–a sacred ritual space–has a greater weight.) There are also examples of oaths being sworn more than once, in more than one place, because they are so important.
Swearing by a particular deity was a stronger statement than swearing by “the gods” in that the oath is more narrowly directed; calling on the deity by a specific (and appropriate) epithet can also be effective. For example, you might swear an oath of marriage to Hera Teleia and Zeus Teleius.
Some people think that swearing an oath will increase the likelihood that they’ll actually do whatever it is they are swearing to do. (I think it is the same principle behind New Year’s Resolutions…) This is almost never the case. If you think you need an oath to get yourself to do a thing, it’s not a good indication that you are at all ready to do the thing. People who ask another to swear an oath for similar reasons will likely be similarly disappointed.
If you are going to swear an oath, to god or to mortal, it’s good to pay attention to how it is worded. Know what it is you are oathing to, because it is in a way a contract. Be specific about what you are promising. Maybe include a time limitation, saying that you will do X for Y amount of time, or that you will do X within Z period of time. A more open-ended oath is not necessarily a bad thing, it can leave room for changes in relationship, but if you make one, be certain that you can fulfill it.