I guess it varies from person to person.
For me, as a polytheist, it is a mix of integral animism that I have always felt, and UPG, or unverifiable personal gnosis. I recognise, unlike some theists, that UPG is not scientific, and is not an empirical argument for my belief. But, this is belief we are talking about, not empiricism.
My integral pull towards a somewhat animist/panentheist theological view has motivated me to think of the world itself as evidence for the divine. Not the "Argument from Design" kind of idea, which I've always felt was something that smacked of Creationism; rather, to me, the gods are as real as the trees and air in front of me, because to my view, they are the trees and the air, and the universe around me.
As to "what" I believe- I believe that there are multiple gods, though they do not directly control the world. I believe that they influence it indirectly through other agents and entities, but nevertheless are felt and should be respected by those who claim to follow them. But, I don't think that everyone should believe the same thing; all people have different views and beliefs, and no one system can satisfy everybody.
But those that do claim to be theistic should respect the god/s they worship and believe in. Not everyone should belong to the same religion, but if you do belong to a religion, you should follow its tenets and be respectful of them, or else find a different one that suits you.
