Here's how it works. Let's start with the first row. The basic form is "a-", but let's use a full word right away so that there are more associations for the brain to work with. Pick any root you like, it really doesn't matter. Let's say -k-, which means "PATH-ORIENTED TRANSLATIVE MOTION" (anything from go, come, leave, arrive, etc). So the basic form then is akal (the second a signifies oblique case (the default case), and -l is the default value from Table 5 for the Ca affix); in general, adding -al gives you the most basic meaning of any root.
So: akal. This is our basic form which we will "conjugate" into the three other Functions: dynamic, manifestive, descriptive (see the grammar if you don't already know what these functions do!).
akal conjugated into dynamic function is ikal.
akal conjugated into manifestive function is uikal.
akal conjugated into descriptive function is oikal.
akal ikal uikal oikal
Familiarize yourself with these three conjugations (which make up one conjugation pattern). It also helps if you think about how the meaning changes when you conjugate the word, so that you begin to associate the meaning with the sound.
Each conjugation pattern can be learned in isolation, or they can be learned in groups of three, whatever suits you. I learned them in groups of three (I wrote them on three different colored cards and then just carried them around with me), because they do happen to share a few, uhm, patterns (that word again, this time meaning something different again). What I mean is that, for example, e- -> ai- (2nd conjugation pattern), and u- -> ei- (3rd conjugation pattern), sort of work in parallel (the two dynamic forms are similar). If you can possibly make yourself see patterns in the Patterns (that old pun again), then do it.
If you can, make up words with each different conjugation. Real words help a lot. After seeing the aidhawél example in the grammar I never forgot that ai- is the dynamic function (of some base form). Later I learned that aidhal is a conjugation of edhal, which is the base form of the second conjugation pattern, as you can see above.
The point of all this is that you don't have to learn the table values as random intersections of three different categories, but instead learn a set of (nine) independent conjugation patterns. At least for me that's much more cognitively comfortable.
What does one get out of it?
Now that I have internalized all the stem-pattern-function conjugations, I can look at any word and know straight away what Function it's in.
Any word that I know in the basic stem form (i.e., the stative form) I can immediately "conjugate" into any of the other Functions (dynamic, manifestive, descriptive), depending on which one of the nine conjugation patterns it follows. Knowing that êqal means "woman", I automatically know the other three forms ieqal iùqal üeqal.
This skill is very useful, and I recommend learning it very early on, because it unlocks the entire dictionary for you. You can go to http://ithkuil.net/lexicon.htm and immediately know all the forms of each root without having to painfully consult the basic morphology chapter each time you want to make a word -- a huge time saver, and it gives you a nice feeling of autonomy.
Finally, here is an even more simplified version of the above table, cutting out everything but the "unconjugated" forms. That way it actually works as an overlay for the dictionary entries, unlike the rather crowded table above.
I wish you good luck!