Prayer is the most important ritual form in Ancient Hellenic religion. Ancient Greeks were polytheists and understood themselves as being in relationships with the Great Ones who they called the Theoi—the Gods. These relationships were both individual (between an individual and one of the Theoi) and collective (between society and one of the Theoi or groups of Theoi). Many rituals are about creating, strengthening, or restoring the healthy bonds of relationship between humans and any of the many spiritual beings. Sometimes the prayers ask divine beings to intercede, such as in a healing or mystery initiation. Because there are many Gods, the ritualist must specify for whom the ritual is intended and get Their attention. This is what prayer accomplishes. Prayer is, therefore, the cornerstone of Hellenic practice. It is a required part of every ritual, but it can also be a stand-alone sacred act.
The model of prayer I use is derived from the ancient Hellenic traditions. Because it assumes that the Gods are real beings, it also requires some preparatory work until you have successfully built a strong personal relationship with whichever deity you are praying to.
Preparatory Work
1. Determine Who and Why
You need to decide who you are going to call (because a prayer is rather like making a phone call), sometimes with a request for the recipient to be present in the moment, as in an invocation. Clarify for yourself why you are calling the particular to whom being you will pray. It can be just to express love and gratitude for a deep relationship you already have or it can be that you want to reach out and express interest in building a relationship. If it is to ask Them to do something or to participate in a larger ritual complex, you need to contemplate how it fits into Their agenda. Ask yourself why Deity X would want to show up in this context and be ready to make the case as part of your prayer.
2. Gather Background Information
All of the really big Theoi have a lot of aspects. Apollon, for example, is a healer, a prophet and counselor, a musician and leader of the Muses, a hunter, a law-giver, the patron of young men, a purifier, a patron of philosophers, often a divine ancestor, a patron of various regions and cults, and is the Lord of Light and is sometimes understood as the spiritual being whose body is the Sun. All of these aspects have epithets—additional names that hone in on the specific attributes. For example, when I pray, "Apollon Maleatas, Iatros, Iatros!" I'm calling Him in His aspect as a healer. That call sends up a particular flare where Apollon can perceive it and He understands which of the many roles He fulfills that I am calling for.
It is also useful to know if you are calling to an empyrean (highest heaven) or chthonic (Earth and underworld) deity or aspect. Many of the Theoi have both aspects, but often have defaults. So, for example, Zeus Meilichios is a chthonic aspect of Zeus, but Zeus is almost always empyrean. If you are calling on a chthonic aspect of Zeus, you probably know it. If you work with a particular being regularly, it can be useful to have an enlivened statue dedicated to your regular communion.
3. Gather Any Offerings
You don't have to give offerings with every prayer, especially if it is a simple prayer of communion with one of the Theoi with whom you have a strong relationship. If you do want to make offerings, determine if they will be burnt, poured, buried, or left outside. Traditionally, libations can be poured to empyrean or chthonic deities. Food/liquid offerings were traditionally poured into a hole in the ground for the chthonic gods whereas food and incense were burned for empyrean deities. In our current contexts and living arrangements, we often leave food outside rather than burning it or burying it. I think that is fine. I typically restrict myself to libations and incense because I live in an urban apartment. While there are some traditional offerings for various Theoi, there are a lot of substances we have now that were not available to the ancient Greeks which They might also enjoy. I advise seeking guidance from your intuition about what to offer whom, while obeying the basic rule that, if you wouldn't enjoy it, don't offer it a god.
Praying
While there are not hard and fast rules, there is a general pattern to Ancient Greek prayers. All prayers should ideally be spoken aloud. Ancient Greeks associated silent prayers with making shameful requests. While there may be situations in which praying aloud is impossible for safety or other reasons, speaking aloud is part of what gets the energy moving, sending a beacon into the spiritual world. You also want to pull up as much emotional power as you can in order to send out sympathetic resonance to the Great One whose attention you are trying to get.
Steps:
Prayer Practice
If you are striving to build a relationship with any of the Great Ones, I encourage you to develop a regular prayer practice. The form of prayer discussed can be elaborate or simple, but the act of calling to and connecting with the Theoi is essential to having a relationship with these beings. You can make a simple call to one of the Theoi, asking Them to attend because you long to build/strengthen a relationship with Them. Your request is communion or to accept your offering. Then ask Them to send you a sign that They are pleased with your relationship. Sit and see what comes up. Thank Them for coming and then go about your day being open to signs from Them. The point in relationship-building is regular contact, not elaborate rites. In my experience, if you build the relationship through the regular prayer practice, it is far more likely that They will show up and work with you in bigger rites.