I think you are asking specifically about practical LLM engineering and not the underlying science.
Honestly this is all moving so fast you can do well by reading the news, following a few reddits/substacks, and skimming the prompt engineering papers as they come out every week (!).
I strongly recommend playing with the OpenAI APIs and working with langchain in a Colab notebook to get a feel for how these all fit together. Also, the tools here are incredibly simple and easy to understand (very new) so looking at, say, https://github.com/minimaxir/simpleaichat/tree/main/simpleai... or https://github.com/smol-ai/developer and digging in to the prompts, what goes in system vs assistant roles, how you guide the LLM, etc.