How do you use the ultima weapon in Final Fantasy 6?

You just equip it like any other sWord (remember, not all of the characters can use SWords), make sure you manually equip it - due to the way it works, Optimize will never equip it, even if it's currently your strongest weapon.

That is because the strength is determined by the current HP of the wielder. A character with 9999 current HP will hit the strongest, using it. If the character is wounded down to 1000 or so, the weapon's power will be greatly weakened.