Although it's no longer used in official tournament play the Multi format does still exist, for 3-5 players (once you have 6 you split into two groups of 3).
Going first (or rather, deciding who has the right to choose who goes first) works the same as in 2-player; any random method like a die roll will do. Once the starting player is decided, turns rotate clockwise starting with them. Instead of 2-player's rule that the very first turn of the game has no draw phase, in Multi no one gets a draw phase for the entire first round (meaning whoever went first will also draw first, but on their second turn).
On your turn, you may challenge whichever other player you like. Abilities that specify "opponent" or "opponent's" refer specifically to the opposing player in battle, but cards that specify "opponents' ", "other players", or something to that effect target all other players. Note that players not in battle can still act, such as using Dominants or triggering an already-played card like Gamaliel's Speech to interfere with the battle.