Radio work was probably the most challenging thing for me in the beginning learning at Teterboro seeing as nothing there is standard for single piston VFR, so a lot of focus was on comms. The good thing was that I got exposed to a lot of different things inthe beginning and feel confident pretty much anywhere.
LOL- I hear you- I also started at KTEB... even just over ten years ago, it was not the friendliest place for novice bug-smashers. But yes, very educational. I was also lucky to solo and then do more training at (uncontrolled) N07, where I learned even more (mostly what NOT to say), then returning to KTEB to finish up.
As for what should be taught and how, here's my non-instructor's 2 cents:
It's possible to be too pro-active. I had a couple of CFIs back then who were the Nervous-Nellie type, always playing with the radio or telling me what to say instead of letting me practice (it's very much a mater of acclimation), but my first two instructors simply had me listen to them a few times and encouraged me to soak up all the other calls on the various freqs... I found this a much better way to learn, and they told me I adapted very well. My second instructor even used to always say "damn, you're better than I am on the radio!". I think I learned an awful lot about timing and cadence listening to those KTEB controllers, who could go on like auctioneers sometimes yet be well-understood. Controllers seem to like it when I take pains to make my calls as they do... I tend to follow their lead and defer to their judgement on how to use the radio because after all, the average cab or TRACON controller makes many, many more radio calls in a given period than any pilot.
And a couple of good long flights with multiple stops at unfam fields and a call or two to Flight Watch while under Flight Following should clear up the freq-juggling and jargon-spouting jitters for any noob radio-user. From what I've heard out there it does not always do the trick , but it should...
It's really not that complicated: as long as you accurately spit out Who, Where, and What, listen to everything on your freq and not just your tail number and read back what's supposed to be read back, you won't do any damage.
And one more thing: don't argue with the weekend crew in the Brown Muni tower in San Diego; they keep a copy of the FAR/AIM handy (no it wasn't me).