The new skill is programming, same as the old skill. To the extent these things are comprehensible, you understand them by writing programs: programs that train them, programs that run inferenve, programs that analyze their behavior. You get the most out of LLMs by knowing how they work in detail.
I had one view of what these things were and how they work, and a bunch of outcomes attached to that. And then I spent a bunch of time training language models in various ways and doing other related upstream and downstream work, and I had a different set of beliefs and outcomes attached to it. The second set of outcomes is much preferable.
I know people really want there to be some different answer, but it remains the case that mastering a programming tool involves implemtenting such, to one degree or another. I've only done medium sophistication ML programming, and my understand is therefore kinda medium, but like compilers, even doing a medium one is the difference between getting good results from a high complexity one and guessing.
Go train an LLM! How do you think Karpathy figured it out? The answer is on his blog!
Saying the best way to understand LLMs is by building one is like saying the best way to understand compilers is by writing one. Technically true, but most people aren't interested in going that deep.