Yuna's Celestial Weapon - Nirvana
If you didn't already know, in order to complete any of the Celestial Weapon quests in Final Fantasy X you'll have to first obtain the Celestial Mirror. Once you've obtained the Celestial Mirror you'll be able to open the chests that contain each character's Celestial Weapon as well as power them up in Macalania Woods.
Yuna's Celestial Weapon, Nirvana isn't very difficult to obtain but it is extremely time consuming. For this ultimate weapon you'll need to obtain all three of the optional Aeons, Yojimbo, Anima and the Magus Sisters. Acquiring Anima requires you to complete all 6 of the Cloister of Trials Destruction Sphere parts which is arguably the hardest part of this quest.
To obtain the Nirvana base weapon you will need to visit the Monster Arena in Calm Lands and speak with the guy there. He will explain how the Arena works and ask that you capture 1 of each type of monster in the Calm Lands. This is quite simple, all you have to do is wonder around the Calm Lands killing monsters with the weapons you buy from this guy equipped.
There are a few species of monsters in the Calm Lands which only spawn in the northwestern part of the map (around where Tidus' Caladbolg is located). If you are interested in learning more about the Monster Arena or are having a tough time locating the monsters you need in the Calm Lands I recommend you check out that guide. Capturing monsters is extremely important to maximizing the potential of your characters.
Once you capture all the monsters you need in Calm Lands speak with the guy at the Monster Arena again and he'll spawn a chest nearby. You'll need the Celestial Mirror to open it of course and once you do, you'll be given Nirvana.
The Moon Crest is pretty easy to obtain and there's a good likliehood you already have acquired it around the start of the game. Check your Key Items before taking the airship over to Besaid so you don't waste the trip!
If you don't have the Moon Crest then take the airship to Besaid and swim north into the water. One of the alcoves off the harbor will have a chest in it and inside that chest is the Moon Crest. If you need help finding it take a look at my screenshot below. Click on the picture to enlarge it if you're having trouble seeing my minimap!
In order to obtain the Moon Sigil you'll first need to obtain all 3 of the optional Aeons. After you do this you'll have to fight Belgemine in Remiem Temple which is the same location we came to in search for the Celestial Mirror and the same location we obtain the Magus Sisters. In fact, you have to defeat Belgemine a few times in order to obtain the Magus Sisters from this temple. More information is found in that guide.
Essentially this part is really a complete pushover, all of my Aeons one shot Belgemine's Aeons - the hardest part of collecting the Moon Sigil was obtaining all 3 of the optional Aeons first.