The practice of Tarot reading is as genuinely fascinating as it is widely misunderstood. If, when you picture the practice of Tarot reading, you imagine sly-eyed Romani travellers and teenage goth girls smoking clove cigarettes as they shuffle artistically battered decks, you're not alone.
Pop culture, combined with tv psychics and the kind of Witchcraft 'practitioners' who give the rest of us a bad image by claiming mystical powers, have soured the practice.
Tarot has been around for centuries, the first known deck having been discovered in Italy in the 1530's, and psychic powers have absolutely nothing to do with the ability to read them. Tarot is what is considered a tool for divination in the same way that China's I Ching is (I Ching has been around since 9th century BCE).
In Tarot, each card has a unique meaning; depending on which cards are pulled and in which 'spread' (the design of how cards are laid out adds another layer to the reading and helps focus the intent down to specific interpretations), the reader is able to decipher what ought to be a sort of oracle from each card pulled and how it is arranged.
You don't need 'psychic' ability, because the idea of the reading is that it is predicated on fate; you pull the cards you were meant to pull in order to read a message ostensibly sent by your Higher Power.
I'm not great at the Tarot, there's 72 cards and every single one has a specific and unique meaning associated. It's difficult, but it's not impossible and absolutely no psychic powers are required.