The Structure of a Pagan Prayer
When appealing to a deity or making an offering, it’s wise to know how this was traditionally done in the past so you can be as respectful as possible and build a true reciprocity with the gods. This type of prayer structure is found in all manner of pagan religions from Norse paganism, Hellenic (Greek) polytheism, Kemetic (Egyptian) prayer and so on. I got the inspiration and much of the information here from @Ocean Keltoi on Youtube who is a fantastic scholar and Norse heathen who actively stands against prejudice and is all around a wonderful resource.
Now, there are three main elements of a pagan prayer, which should be done in this order:
1. The Invocation. This is where you call upon the specific god you’re hoping to connect with. Think of it as writing the name and address on your letter to the Gods - it lets the deity know that this prayer is directed at them, which is important in a polytheistic religion with many gods. To start your invocation, address the deity directly by name, or use an epithet or kenning that they're known by. It's especially wise to choose an epithet that relates to what you're praying for, like using one of Apollo's healer epithets while addressing him in a prayer about a loved one's sickness, for instance. It’s also a good idea to praise them highly and with a certain air of reverence. These are ancient deities after all.
2. The Argument. Here you give your reasons for why a deity should fulfill your request and favor you. If you’ve brought offerings, cite them here. You can also include reasons for why you’re reaching out, such as love in a prayer for Aphrodite or matters of justice with the god Tyr. This is where you make your case to them. And if you’re reaching out to a deity you don’t have a working relationship with, which let’s be honest will be the case many more times than we’d like, then you can tell them this here also. A good example might be “Oh Tyr, one-handed war god and son of Odin, though we have not met before I have heard your name and been called to it…”
3. The Request. Finally you ask the gods to look kindly on your request and to grant you their blessing. Again, be as respectful and reverent as possible towards them.
Prayer Example: “Grey-eyed Athena, daughter of thundering Zeus, if ever I have poured out sweet wine for you, look kindly on me and grant me your wisdom.”
How to stand when making the prayer
This depends on which God you’re reaching out to and, of course, your own personal comfort. The most common ways of praying are to stand and perform some gesture of reverence, kneel while praying and even prostrate, kneeling fully on the ground with your head down as you appeal to the gods. Some might also choose to wear veils when performing prayers or rituals for deities, though this is naturally up to the individual.
In Hellenic tradition, if you’re praying to an Ouranic god (deities of the heavens) you would traditionally wear your hair up and stand with your arms raised to the heavens while reciting your prayer. Meanwhile, if you are praying to a Chthonic god (deities of the underworld), you would kneel and face downwards towards the Earth with your hair flowing freely.
Some Norse sources tell of ancient pagans prostrating before the gods, and yet this is still not entirely necessary. Pray however you see fit and what is most comfortable for you at the moment.
^ This is what prostrating looks like
Ocean Keltoi's video on pagan prayers
Hearth and Fire Work's blog post on Hellenic prayer structure