Witchipedia

Different people have different beliefs about this. I do not believe that spirits have anything to do with Tarot cards, but there are others who believe passionately that they do. I have had these arguments, and I have my doubts as to whether Tarot is actually magick at all (rather than psychology)- I actually had that argument in one of my Anthropology classes. I can only explain how I believe Tarot cards work, based on my own experience.

Each of us has a subconscious mind, a feminine mind in occult terms. This mind takes in everything we experience, everything we see, hear, smell, and every genius idea we have. If we walk into a room and only notice the hottie over at the buffet table, our feminine mind has already noticed every other guest, the décor, the music and everything that's on the buffet table. We can turn around and leave the room and remember only that the hottie was there, but our feminine mind knows everything and everyone that was there.

With all this information, our subconscious mind can figure out a lot of things that our conscious mind simply never notices. There are several ways our subconscious tries to tell us what it knows. Funny "feelings" deja vu, dreams, etc. Many inventions and scientific discoveries have been triggered by a dream, that is, the researcher's subconscious put a bunch of stuff together without them noticing and then communicated it to the conscious mind in a dream.

What does this have to do with Tarot?

Well, one of the ways the subconscious mind can communicate with the conscious mind is via symbols. Some of our symbols are universal in our Western culture and Tarot artists do a wonderful job of putting these into the cards. So when you read Tarot cards, you're really reading messages from your subconscious mind. Things you don't know you know.

I know it seems that this could only work when you're reading for yourself. Enter the theory of the collective unconscious; The idea that all of our subconscious-es are connected. If you are like me and you believe that we are all made of the same "stuff" and thus all energetically connected anyway, this makes sense. There is the Jungian idea of the collective consciousness and the idea of Akashic records, so I think the idea of my subconscious talking to your subconscious through the medium of symbols on the Tarot cards isn't so far fetched. I've ended up in other peoples dreams, people have ended up in mine, so why not?

As for spirits, well, I think if you work with spirits and they wanted to talk to you they would use whatever means is at their disposal. You don't need them to read cards for yourself or another person, but if you wanted to communicate with them and you didn't have another means, there's no reason you couldn't do a reading for them as a form of communication. But, to read someone else- the symbols of the Tarot are the language of the subconscious (well A language) and you can learn it without spiritual intervention. That being said, Spirits are often willing to teach us things, so if you're having trouble with the Tarot on your own, by all means if you have spirit guides, friends, patrons, etc. ask them to you help you out.

Like morning bird said up top there are different beliefs about what exactly is communicating through the cards and s/he did a great job doing so., the only thing I can think to add is my own personal belief.
Everything has an energy, or in my words, a personality. To me the cards are their own unique spirit, different to living things but still relevant. So when I ask a question I feel like I'm asking the deck itself for its opinion/view/experience.
I will say though that no matter what your belief, there is a bit of psychology involved due to the fact that the cards are a set of abstract ideas that convey an entire number of meanings, it's up to the reader/querent to decide what meaning in the card is relevant and what meanings are excess to the situation.
Meaning that sometimes there can be… for lack of a better word, miscommunication.

Tarot cards are paper. Just like Ouijia boards are cardboard. They’re just a tool just like a candle or talisman. It’s what you put into them and how you use them.
Tarot can be read, and successfully I might add, how Morningbird describes. They can work similarly how our dreams work by revealing and bringing our subconscious knowledge to the surface. But they can also be a means of spirit communication. I do readings both ways. But I will say if you’re going to allow them to be a channel through which spirits relay information to you, you should probably be clear or informed about which spirits are giving the information. But in my experience you can potentially receive a lot more hidden information through spirit communication, but the spirits who are willing to share the most don’t do it for free.