You use Azura's Star the same way you would use any Soul Gem. When you kill an enemy with a Soul Trap weapon or cast a Soul Trap spell on them, their soul will fill Azura's Star upon their death. Then, in the enchantment menu, you can use it to either enchant a new piece of gear or refill a currently enchanted weapon. Unlike regular Soul Gems, however, Azura's Star will not break after use, allowing you to refill it.