Finding Meaning
I'm one of those that does not believe there is any inherent "power" in a deck of tarot cards, at least as far as divination is concerned.
Whatever power of divination exists, I believe it resides in the reader, not the cards.
Because of this, I begin my own readings by invoking Hagia Sophia (the spirit of Holy Wisdom) to guide me, inform me, infuse me, etc. This is to enhance my reading of the cards, not to somehow empower the cards. Other things might work for other people, to focus the mind, etc.
Not to bore regarding archetypes and such, but they do "speak" to us in their universality. People have a way of seeing patterns in many things, be it coffee grounds, textures of fabric, or clouds. We can actively improve our ability to extract meaning from these patterns, given practice, the right frame of mind, creativity, and insight. Call it intuition if you will.
Tarot cards are a tool, and a good one, to enable the human mind to clarify image and pattern, and to locate the meaning that may lie therein. In theory at least, a person who was truly adept could identify meaningful patterns without using the cards at all. For most of us, the 78 cards in various combinations are quite sufficient. For the most part, tarot is really about insight into ourselves or others.
I hope I'm not being too obscure. In the end, I doubt religious/spiritual beliefs, or the absence of them, really matter in tarot...except as they dispose each of us individually as readers. What works for one may not for another. We each must find and explore that path that works for ourselves.