I don't know if it's the best way, but what I did was get a blank book and divide into 78 sections, and I just started gathering meanings of each card from all sorts of sources. Also added little notes about what some of the images were in the cards (I started with and still mainly use RWS decks). I would sit with a deck and test myself by saying aloud a keyword for each card as I turned it over. If I got it at once, I'd put it in one pile. If I hesitated or didn't know, I put it in another pile. It wasn't just the key work I was after but that confident feeling inside that I understood the nuance of the card. Then I'd go through the 'other' pile and if needed look up things in books. I used to just sit and do this while watching television. (In fact, I still handle decks every day, but I don't have to play the flashcard game anymore. I do sit and study cards from various decks every night, though. Just looking at, thinking about, staring at them. Okay, I'm a bit obsessed!) I also did practice readings using the books. I'd look up meanings as needed, then look at the whole spread and practice stringing them together in a story. I read for fictional characters, my stuffed animals, imaginary clients. Then I found AT and started exchanging readings with people. All the while I was reading tarot books. (And accumulating decks!) After a few months, I began forcing myself to read without looking in a book. I would sometimes look things up after to see if my interpretation was close to any book meanings (I would use my personal journal because each card had lots of meanings I'd gathered from all kinds of sources, so I could see the range of interpretations from various readers). I was studying pretty intensely, though, and you might take longer--or shorter! I'd say by 6 months I was able to read without consulting books. When I'd been reading a year, I went to a tarot conference where seasoned readers at my table expressed surprise that I'd only been reading a year. That was a real confidence booster.
As to being psychic, I do not consider myself psychic. However, I am open. I trust the universe, and I trust the tarot as a tool to channel those energies into my mind. I trust what comes to me during a reading. I don't know--does that make me psychic? I never see ladies in purple hats!
But I almost always seem to get to the heart of what the querent is feeling, so I suppose that is something. I know I have a long way to go, it's still early days for me.
Good luck in your tarot journey!