Early in the game I use items, late game it's all magic. I always heal my guys outside of battles so I don't have to waste battle turns curing. In FF6, I have Cure Rings on all my guys (which casts regen). With bosses and tough monsters, I'll cure when my guys lose 25% health or more (I'll target all characters for cure, unless a specific person is near death). When my guys get low on MP, I'll steal some from the enemy (Osmose).

A common newbie mistake in any RPG is not keeping your characters healthy. That's the first priority (your guys can't attack if they're dead). Don't wait until it's too late to heal your guys.