I am, as I will freely admit, not a woo person. On the whole I am fine with this–from what I have observed, having an active godphone is not a thing that makes people’s lives easier. But it is a definite disadvantage when you are trying to work out what it is that the gods are trying to tell you, or even trying to figure out whether what you are doing is working, or appreciated, or even appropriate.
I would love to be able to tell you I have figured this out, but I have not. My godphone is generally out of service, and when it is, the signal clarity is minimal.
What I’ll try to do here is discuss a few tools that might be useful for you if you, like me, are trying to figure this stuff out.
Research
This may not be in everyone’s toolbox, but as someone with a semi-reconstructionist methodology, and as someone who isn’t all that trusting of their own intuition, it’s at the top of mine.
Research has the benefit of (relative) solidity. It isn’t necessarily quantifiable per se but it provides tried-and-hopefully-true information. If myth tells us that the peacock is beloved by Hera, it’s an indicator that using peacock imagery in creating sacred art for Hera might be appreciated. If history tells us that libations of wine were poured out for the Olympian gods, we can probably be comfortable making such offerings to those gods in most circumstances.
Of course, all research is incomplete. There are, for example, varying accounts of how offerings to the dead were made and what those offerings may have consisted of. I’ve not found a consensus that I am comfortable with and I think that’s probably because no such consensus ever really existed.
It’s likely that much of religious practice varied both regionally and over time, and it’s probable that there is plenty of knowledge that has simply been lost because it was never recorded or because those records did not survive the centuries.
Primary sources–texts such as epic poetry or hymns–are the gold standard of resources, but they are not always easy to interpret. Archaeological evidence on its own can be even more difficult if you are not a trained archaeologist, and I am not.
There are some very good secondary sources, scholarly sources that are also accessible to the lay person and I’d suggest looking at a few different ones, keeping in mind of course that archeology is a science and scientific hypotheses change as new evidence appears. Walter Burkert’s Greek Religion is a very good overview that’s often recommended; my personal favorite to suggest to new folks is A Companion to Greek Religion, edited by Daniel Ogden, which includes a selection of good articles on a number of different aspects of Greek religion and the state of current scholarship. I’d also recommend a few scholars as particularly accessible, including Jan Bremmer, Sarah Iles Johnston, and Jennifer Larson. Keep in mind that these folks are not theologians and are studying the religion from a historical and/or archaeological point of view, not a religious one; I’ve never found this to be a problem but I know some polytheists may.
I would never recommend that someone base their practice entirely on research, but it’s an excellent place to start, particulary for those of us who lack easy access to the more esoteric ways of knowing.
Divination
I’ll confess that divination is not my first choice, personally. I started reading tarot cards when I was twelve years old and I am pretty comfortable with the process, but the older I get the less interested I am in divination in general (for the most part) and I rarely use it for this purpose these days.
That said, there’s a lot to be said for divination in that–depending on the method you choose–it can be relatively precise and somewhat quantifiable. Maybe use the scientific method (cognitive dissonance aside :)) and keep records? You can also use a more intuitive method and keep it open to your own interpretation, if that is what works for you.
It is also, for those with anything of a recon bent, something that can be done with a greater or lesser connection to a given culture (alphabet oracles for Greek, runes for Norse, ogham for Irish, etc.).
I’ll include in this section the act of consulting with a more experienced diviner for your answers. If you know someone whose abilities you trust, that is certainly an option. There are articles elsewhere on how to find and choose someone to do this sort of work for you so I won’t discuss it here.
In any case, whether you do your own divining or seek out a seer, I would suggest not basing decisions entirely on a single reading. Get a second opinion, do some research, compare notes with other folks.
Trial and Error
This is exactly what it sounds like–you try something and see how it seems to go over. What are the results? Does it work? Does it kind of work? Does it fail utterly?
As an example, about a year ago I wanted to start making particular offerings to Hermes. I knew I wanted to offer a particular drink just for him, and that I wanted it to be appropriate to the god. So I did some research and found that in some regions of ancient Greece strawberries were sacred to Hermes. I also felt like it should have a bit of a kick to it–so, strawberry vodka. (It was, yes, a “head decision” but I am really a “head person” and many if not most of my head decisions have turned out well. This one, not so much.) A few weeks later, the bottle was gone–no, not empty, gone. It had disappeared. It was not there to make offerings from. I decided to take the hint. Went to the store and found my attention drawn to cinnamon whiskey. That’s what I’ve used ever since and it seems to go over really well.
Your practice doesn’t need to be set in stone from day one; it’s absolutely okay to try different things out before establishing them within your practice. It’s absolutely okay to try new things, to make changes. How will you know if you don’t try? So, try a different prayer, a different offering, a different time of day for ritual. Little changes, big changes, see what works!
Sense and Feeling
“I have the feeling that…”
“I get the sense that…”
This was, for me, the advanced stuff. I am not, as I said above, someone with a lot of woo skills. But if you spend enough time (and for me “enough time” was something like ten years) with deity, sometimes you’ll start to pick up on a few things here and there.
I’m including it here, even though it’s not really an easy tool, because I think it needs to be included. My ability to know things in this way is pretty limited. Maybe other folks have the Swiss army knife of psychic ability and I have a blunt spork, 
but I do have that spork, and sometimes I am even able to use it!
