Believe or not, I am very interested in how people decide what is true and what isn't. I know my method but it makes me curious how others come to gain knowledge.
How did you come to accept deities as real?
I sometimes wonder that myself...how people come to decide things as true that is.
To abridge the story a bit, I used to Christian. I still think Christ existed, but christianity has seemingly forgotten Christ. I always found the idea of one totalitarian god rather uneasy, as there is no such thing as a benevolent dictator. I simply could not stomach that there was only one god, and that a world view that came from some place in the desert was the all-encompassing truth of all.
I found Asatru through searching various sources. I found it rather appealing, the code of it, the feel of it. I had never been the "bow your head, and be a sheep" type. I found that my ancestry came from northern and western Europe, and thus, the gods of Asatru were actually the gods of my ancestors before Christianity used the sword and fire to try and destroy it.
Now, as for believing them to be real, well, I can go off personal experience a bit. When I pray to the gods, I feel as if someone is listening. I will not say that everything is answered, but I feel that someone is at least picking up the phone and letting you speak your request. My first prayers were answered rather greatly. And I continue to feel a kinship with the gods. After all, I identify with them far more than the deity of Israel.
All that may not be very convincing. I am not really a good apologist. That is not really what I aim for. I do not think one can accept things like that as real without at least some faith. And to be honest, that is enough for me. If they are indeed fake, then I still lived my life with as much honor as I could. I can die with a smile on my face with that thought. Whatever inspires you to live nobly is acceptable to me.
I hope that can at least somewhat answer your question.
PS: Want a little fun fact? The god Yahweh, the one that Judea-Christians usually call their deity and claim he is the only god, is actually the Hebrew Storm god from the original pantheon. He was essentially "upgraded".