How does the Dual Enchanting Perk work?

If I get the Dual Enchanting Perk, can I add an additional enchantment to an item that I previously? Similarly, can I add an extra enchantment to an item that I didn't enchant, but found already enchanted?

No and No.

The Extra Effect perk only works for newly enchanted items, and both enchantments must be applied at once. You cannot enchant an item that is already enchanted.

You can, however, disenchant an item to learn that effect, and then apply it, along with an additional one to a new item of your choosing. Seeing as you'll have a 100 Enchanting Skill at this point, the item you create is almost certainly going to be better than the one you've destroyed to learn the effect anyway.