You can't gain skill exp when your using normal attacks, use skills when grinding skill exp. You can transfer sword skill exp to magic exp and so as magic to sword. It's on second warp in Port Lux and its where you can also buy new skills. You can gain skill exp on training dummies but i strongly suggest on hitting the mobs. I've tried the invisible dummies on chaos arena but it only gives little skill exp thats why it's better to grind skill exp on mobs. Forgotten ruin and undead ground is a good spot to grind skill exp.
Hint: Don't grind skill exp, you'll achieve dual trans and not knowing it by questing the ranks.... it's better that way.