Azura's star is from a quest found at the shrine in the Northwest part of the map (near Winterhold I believe) Asking about rumors from inkeepers can sometimes get them to put the location on your map. The quest from the shrine first has you go find it in a sunken fortress. Once you aquire it you realize that it has been broken so you can either take it to a mage or back to the worhiper at the shrine. It is HIGHLY recommended that you take it to the mage and turn it into a black soul gem (allows you to capture human souls).
The best way to capture a soul is to enchant a weapon with soul trap on it that way anything killed with the weapon will fill a soul gem. Nearly all creatures have sould (dwemer robots don't) and can be captured. The higher the level of creature the greater the soul is. Souls automatically get placed into the smallest possible soul gem that they can fit in. With the Black Azura's Star you can soul trap humans wich are all Grand Souls. Unlike other soul gems Azura's star is re-usable.
A great way to level your enchanting is to use a weapon with soul trap on it and kill human bandits. After you kill one, use Azura's star to re-fill the weapon enchantment. Wash, rinse and repeat.
I think I know what the OP is saying as I am having trouble filling it as well.
I completed the quest at the shrine and received the fixed Azura's Star but I cannot put a human soul into it. It sits in my inventory, empty. When I kill humanoids to take their souls I get a message saying that I don't have a soul gem large enough for it. Is there something else that I'm missing?
EDIT: Apparently I did the wrong thing by taking it to Azura - she does not give you the Black Star. Only Nelacar can give you the Black Star.
"Maybe the bullet insulted your little sister...missing your bionic turkey leg...it really hurt your feelings [for] -147 hit points?" SavingPrincess