I imagine it's simpler to write Minecraft mods but I'm also curious about more complex ones like how FPS aiming/firing cheats work. Or Runescape-style repeat-activity cheats.
How did you learn how to write game cheats/mods?
Where would you recommend an experienced programmer start today?
Find a game you like (preferably that has a modding community already), decide to make it do something it doesn't do yet; and go to it. Find an existing mod that's close to what you want and try to make it stretch to your vision. Look at all the mods for your game you can stand to, and see how others write theirs. Be prepared for some horrors due to non-experienced programmers "getting it done" with no idea how or what they're doing.
Then go find a different game and discover how varied the experience can be :)
Factorio is great for diddling with, very straightforward, fully (and excellently!) documented, voluminous examples of all manner of ideas already implemented.
It probably won't be that simple for most multiplayer games or those with anti-cheat protections, but it was super enlightening for me.
Honestly if I was making multiplayer cheats I'd probably just use a camera pointed at the monitor and emulate USB inputs. That would be quite difficult to break with anti-cheats. That said, I don't feel like ruining games for other people. Single-player though I feel no qualms about modifying.