What is the best way for an individual to advance the game of chess in the broadest sense?
I can think of two main senses in which I mean that -- increasing the quality of play globally, and improving standard chess theory. I am less interested in chess engine improvement and endgame tablebase generation, which seem to be in good shape. Chess engine improvement has plenty of financial incentive. And tablebase generation is low-hanging fruit intellectually, with plenty of academic support.
The obvious way to increase quality of play amongst players is to teach chess. Under a presumption that serious play improves any person's quality of play, another way would be to run tournaments. In both cases, the easier route would be to join an existing organization rather than start from scratch. A significant difference between the two is that teaching would require/result in more self-improvement in the game itself.
Finding improvements in standard chess theory does not seem hard. But proving them, and getting them accepted generally, looks much much harder, probably involving at minimum the publication of a book. Just using them in one's own games hardly can make a difference. For just one thing, it requires the cooperation of one's opponent to reach relevant positions. :-)
Any suggestions and advice welcome.