Polytheism, as it happens, is basically a pretty simple concept. All it means, if you say you are a polytheist, is that you believe in and honor multiple gods. That is it, as far as I can tell.
You can be a reconstructionist polytheist, or you can be a totally modern polytheist, making it all up as you go along. You can be a polytheist who follows a particular path or tradition, or you can be a polytheist who uses whatever methods best suit you as an individual. You can be a polytheist who builds your practice from history and lore, or you can be a polytheist who works from instinct and personal gnosis. You can be a polytheist who is a spirit worker with wide-open channels to divinity, or you can be a polytheist who is entirely headblind and must take everything on faith alone. These are all possible things.
Polytheism doesn’t require a particular sort of practice. Some sorts of practice do seem to tend more toward polytheistic belief than others. Most if not all of the recons I know are polytheists. Many if not most of the Druids I know are polytheists. I also know neopagan and Wiccan polytheists. These, too, are all possible things.
Polytheism does seem to require a particular sort of belief, but the specifics of that belief aren’t all that cut and dried. Some folks consider each and every deity name, sometimes including epithets and kennings, to denote a different entity. Some folks consider that different cultures know the same gods by different names (there is some historical basis for this custom–the Romans certainly did it to an extent during their travels). Different people draw the line in different places, and I would hesitate to say that any of them are not polytheists as long as they do identify different gods as different.
I’m a fairly hard polytheist, but I take it on a case by case basis.
Is the Irish goddess Brigid the same entity as the British Brigantia? How about the Gaulish Bricta?
Gaulish Lugus, Irish Lugh, Welsh Llew, all share some etymological link, and the latter two have a known mythological connection as well–are they the same?
Is Odin Woden? Is Thunor Thor?
Is Artemis Elaphebelia (Artemis the Deer-shooter) the same as Artemis Agrotera (Artemis of the Wilderness)? How about Artemis of Ephesus, whose depictions in art are unlike any other?
Zeus Meilichios receives offerings appropriate for a Chthonic deity, while Zeus Olympios (and Zeus under most of his other epithets) receives offerings usual for an Olympian deity. Why is this? And does it imply a difference in identity or simply a difference in office? Is Zeus always Zeus?
(In case you’re curious, for me the answers are no, no, maybe, yes and yes. Mostly due to personal impression. :))
This does make me think that I can’t just say that I am a polytheist and have it mean something at all specific. Knowing that I am a polytheist doesn’t really tell you anything apart from the way I view deity–it doesn’t tell you how I think that deity should be approached or worshipped, it doesn’t tell you anything about my practice or my cosmology. It doesn’t even necessarily tell you how I define a deity. It just tells you that one thing–that I believe in more than one god. Which I do.