What is the best practical guide to training a LLM for a specific task?

I've done some messing about but I now have a couple of very specific tasks/problems in my personal life that look like prime candidates for solving with AI (lots of easily-classifiable data to train it on), and I would like to get clear on how I go about turning that data into a model.

I'm prepared to invest cash into renting machine time on whatever shared host makes sense to use, I don't want to hack this up on a Raspberry Pi, I want to pay for the bare metal resources to implement the best possible engine that is available to me in April 2023.

I have only engaged with this stuff at the prompt input level and I'm already tired of playing with other people's generalized stuff, I want to get real specific.