Go to the Pugilist guildhall in Ul'dah and take the quest from the Receptionist to unlock the Pugilist class on your current character. Once you have multiple classes unlocked, you can switch between them by changing your equipped main-hand weapon/tool. Each class has to be leveled up separately from each other, so you'll go from a level 32 Archer to a level 1 Pugilist the first time you equip the Weathered Hora you receive for that Pugilist quest. (You'll still be 32 as Archer when you switch back to wielding a bow.)

Before you can become a Bard, you'll need to level up Pugilist to at least level 15, but you get a 50% XP bonus on any class below the level of your highest one, so that doesn't take too long.