Chess, it depends on the level of the person you are teaching. If they are an absolute beginner, then obviously what the pieces are and how they move. Once you get there, you start teaching tactics. Some tricks on f7, for instance, quick piece developments, a couple of little tricks they can work on. From there, start them with 1. e4 and teach them the open game. They need to understand piece play. Work with them on some famous games, such as Morphy vs. the Count. Eventually, you will teach them how to open the White pieces (probably with 1. e4 until they get an idea of open piece play), and then defend 1. e4 with 1...e5 and 1. d4 with 1...d5. Anything else, you can teach them the basic setup of ...e6, ...d5, ...Nf6, ...Be7 and ...0-0. From there, you can begin with some other ideas, but it really depends on their level.
How do you be a coach
the key is to cover things from general to specific. It takes a LOT of work to coach well. You have to spend hours studying something so you can show it in multiple ways.
Silman's book on endgames is great for this since you can base your study on whats important
endgames _ rook single and 2 and queen mates are about it
pawns you introduce opposition, square of the pawn , passed pawn, protected passed pawn and outside passed pawn
thats enough for most players when they start out but know them COLD! can you mate with a queen in 10 seconds? 5? how about a rook?
openings play SIMPLE stuff scotch and guccio piano are great since thats what most players face early on.
principles should be repeated time and time again, If a move follows a principle but was wrong tactically thats fine,. point out the tactic but praise the principle.... in time the tactics will catch up.
repeat SIMPLE ideas over and over and over
praise activity
praise development
Yuspov books are great for teaching and give a good layout for anyone to follow
DONT teach opening lines just ideas quote a book for now
I want to be a good coach, but how/what do you teach?