Goblin King is not part of the main quest, it is a tough level 2 enemy, it's part of an unwritten side quests (one of the many secrets the game has/will have). If you cannot use the zzz button, just click on Bell and it should say your current objective, mix it up with what's written on the Journal, and it should give you a pretty good idea on where to go. None of the locations require you to face the Goblin king though, it's entirely optional.
If you still have no idea, just tell me what quest you are on, and I'll let you know where to go.
The stat raising mechanic is the same as DANMACHI, simply do stuff (attack, get hit, dodge, walk, ...) to gather excelia and once Hestia updates your status, your ability score will increase.