How do I enable 2-player mode?

On the Nintendo Switch, to turn on the two player mode in Fire Emblem Warriors, you actually have to use the first player controller to press in the left stick. The second player's controller isn't actually recognized by the game prior to this point.

This will open the controller management menu used for most multiplayer games on the Nintendo Switch and from here you can enable both controllers.

On the 3DS, there is no multiplayer support available (per Rapitor's comment). Heavy has an article confirming this.

The local multiplayer option is only available on the Nintendo Switch version so New Nintendo 3DS owners will have to stick strictly to single-player content.