What do you need to do to become a moderator for a game, and what permissions do you have as a moderator? Just asking

If you request a game to the site and it is accepted, you become the "super moderator" for that game (not to be confused with site or content moderators). A super moderator for a game can also add "regular moderators" for that game.

About what moderators can and should do, and what permissions every type of moderator has, look here: https://www.speedrun.com/moderationrules

If you're the one who requests a game and the game gets approved, you're added as moderator automatically. After that, that moderator can add more people as they see fit. Moderators are expected to maintain the leaderboards for the game.