If you accept the basic principle of psychology (known also before Freud of course but thrown into sharp relief by him): that we humans have mechanisms to suppress, hide, distort, circumvent knowledge which is incovenient, painful or threatening to us, then it's clear that tarot works, and how it works.
Tarot tells us what we know, but we don't know that we know it. Tarot helps us to "lift" little bundles from the sea of the unconscious onto the ship of our consciousness. There are many different tools we can use to access this knowledge, tarot is one among them. Tarot has many advantages: it's flexible, intuitive, easily connected with other tools, and since it's visual, it can access intuitive knowledge not grasped verbally - right brain stuff.
These little bundles of knowledge accessed via tarot can warn me, encourage me, force me to acknowledge uncomfortable truths or comfort me, and explain causal chains I didn't understand before. If we were a more developed species, we wouldn't need tarot cards because we'd use our intuition all the time to assess our lives, actions and choices.
I know that others see it differently and are sure that tarot can bring us knowledge from outside ourselves, but for me, tarot is a self reflective tool and that's how I use it.
I also use tarot to act on the insights it gives me - with affirmations, meditation and visualizations.
To say it with the German poet Hölderlin:
Wo aber Gefahr ist, wächst das Rettende auch.
Where there is danger, there also grows the saving power.
Or in my words: where tarot indicated a problem, it also helps me to find a solution.
And it works beautifully.