(note: these hints may be applied to any RPG,not just the Final Fantasy series.)
Talk to everybody you meet. Some people give you valuable hints to complete your game, while others have a direct effect on advancing the story.
Take heed their advice. If somebody suggests that you do something, you must do it in order to advance the story (i.e. the start of FF4). Conversly, not doing said task may buy you some time to do something else.
When someone from "point A" asks you to go to "point B", report back to point A and tell the person what you have discovered.
Bosses are too tough! try gaining more levels by fighting more random battles. Restore from an earlier save and don't advance the story until you feel ready...you did remember to save, didn't you?
Be prepared. You wouldn't go camping without a tent, now wouldn't you? stock up on provisions with each visit to a town. This is plain common sense.
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