Presumably by writing content that is hyper-targeted at specific questions (e.g. "which is the best X for me to use?") that the LLM will then consume, hoping that it will be regurgitated as fact when the LLM answers that specific question. [I am not an expert on LLM training, so I might be wrong]
This will then mean writing a lot of such content, because hyper-targeted and presumably more repetition = more weighting.
Which is too boring a task for a human. So we'll have an LLM that churns out blog articles that are not designed for humans to read, but purely for other LLMs to read. They may even discover optimisations over "natural" language that improve readability for the target LLM. So we'd end up with half the web being full of incomprehensible junk designed to game search results for commercial gain. So no change then ;)
Presumably, SEO will evolve.
An SEO goal might be to have influence over people, and one method is to game the information systems people use.
Before, the specific methods involved gaming search engines. Right now, they'll be looking at gaming LLMs.