In order to unlock a new hero you will have to find them somewhere in the dungeon.
They Spawn randomly, but eventually you will meet one.
to open the option to hire them, you will have to spend food to hire them.
Once you have hired them, you need to keep them alive and in your party for three floors.
(Or win a game with your new hero, whichever comes first.)
Once unlocked you get to pick your new hero from the starting menu from then on!