When I did my PPL one of the instructors gave us a CD full of recordings that we could listen to to train our ear for it. Matching that to transcripts helped - and it also helps once you know the lingo, since it's mostly a limited set of words and the phraseology has a specific structure.

For example: Altitudes and flight levels:

3,500 is spoken as "three thousand five hundred".

13,500 is spoken as "one three thousand five hundred".

But other numbers (like times, directions, etc) have every digit spoken, for example 10 minutes is "one zero minutes" or wind direction 220 is "wind direction two two zero". Speed reading would be something like "one niner zero knots" for 190 kt.

The sentence structure is also relatively strictly defined, for instance at an unattended airport you would always transmit in this order:

(1) where you are

(2) who you are

(3) what you intend

(4) repeat where you are

So you'd say something like: "Swartkops traffic(1), small Jabiru Kilo India Tango(2), left downwind for runway one eight, touch and go(3), at Swartkops(4)"

This kind of strict structure and limited lexicon does make it understandable after a bit of practice, since you are expecting certain words to show up.