the first 2 output lines show the characters of s paired up with their corresponding elements in levels. The next 3 lines show the ⌸ operator in action: all characters that got a corresponding 0 are in the 1st line, all with ¯1 in the 2nd, and ¯2 - 3rd
I'd say one of the first skills when reading APL is the capacity to parse it. :-) Being a Schemer in a previous life, I'd recommend S-expression-ifying any string of APL code first if you're familiar with that at the beginning until you can do that with 100% accuracy.
I wouldn't recommend trying to read the S-expressions, but simply being able to do it.
Drawing parse trees would also work.
After that, the slow progression through a piece of code on a whiteboard/pen and paper/REPL is useful.
I personally would be suspicious of the technique of introducing intermediate variables into the code as a means of understanding, but if it works for you, go for it.
Maybe a fun game would be for people to study that line of code, guess at how it is used in the parser, and how it relates to the comment about random permutations.