These resources do a good job of explaining how generative AI works.
One of the best ways to get a sense of what generative AI can do is to try it yourself -- no special coding skills required.
Prompt engineering is the term used for process of refining the output you get from generative AI tool, by adding guidance to the prompts you give it (for example, specifying artistic style you want an image generator to emulate) and using a series of prompts so that each answer builds on the previous ones.