I can't really add to what LRichard has said, except about this. A great part of esoteric Tarot is understanding that however you use it, it is a model of the world with active and passive forces, balances and most of all, everything is interconnected. So in fact, some of the most important aspects of the Thoth aren't on the cards themselves.
In terms of Kabbalah, this entails, as LRichard says, internalizing its general structure and what connects to what. Once you grasp the basic method, this isn't as much memorization as it might imply. Astrologically, this mainly means learning the attributions of the Trumps, and what they mean. It isn't actual astrology, at least not until you get to the Courts, but more in the sense of ideas, each astrological element is its own set of them. These two, astrology and kabbalah, together open up whole new worlds that are not apparent otherwise. Although some memorization is part of it, it isn't as much as you would think, since when analyzing the cards you tend to use the same tools over and over, and they become second nature in time.
For example, the Tower is attributed to Mars, and so is the fifth Sephira of Geburah, so all the fives have something in common with the disruptive influence of the Tower. Mars also appears in the Minors, although modified by the signs, and so there is also a connection between the five and ten of Cups, nine of Swords, two and seven of Wands and the three of Disks. What those connections are I can't tell you, it's up to you to work it out. That's where intuition comes in, how you connect all the different elements that are the building blocks of each card.
So you see, it's all interconnected. I'll toot my own horn here, I wrote two introductory essays about these subjects and although they're far from perfect, as well as incomplete, they may give you an idea:
Beginner's Kabbalah: The Four Worlds and the Tree of Life
Beginner's Kabbalah: The Court Cards
We have an extended weekend from tomorrow, so maybe then!
