To acquire Anima, you must first go through a number of task. You have to get each Treasure from the Cloister of Trials from each temple in Spira using the Destruction Spheres, including the one of Zanarkand Dome.

After defeating Yunalesca at the Zanarkand Dome, you receive the Airship and are now allowd to wander Spira until the final showdown with Sin. You need to put in the coordinates 13, 60 (coordinates can vary) In the map, you now have access to the Baaj Temple.

Baaj Temple is the place that Tidus winded up in after the beginign of the game in Zanarkand and where he meets the Al Bhed. Its the same as before, and all you have to do is go over to the spot where Tidus feel into the water and dive in. Of course, there is an encounter with Geosgaeno, which is a pretty easy battle after Yunalesca. Just keep attacking it and keep your partie's HP high. Once you're done with Geosgaeno you can head into the underwater temple. Keep in mind, you must have Wakka, Tidus, and Rikku in your group to have a full underwater battling team.

When you enter the hall before the chamber of fayth, you run into 6 alters with 6 different spheres on them. These are the shperes from each of the temples around Spira. There is also a seal displaying Anima's symbol infront of the door to the chamber of fayth. Activate all of the spheres and you will be able to pray to the fayth. If you have not obtained all of the items from each temple, then hop back in your airship and return to the temple. You may do the Cloister of Trials again in every temple in Spira, and if you make it to the fayth, they will give you items to help in your fight! The only Temple you may not return to [i believe] is Bevelle.

Unfortunately at this point you could have only activated 5. The last one is the sphere from the Zanarkand, which you cannot get without returning to the Zanarkand Dome after getting the airship.

So, return to Zanarkand, head to the dome (there are little transportation pads that you can use to get there) and go through the little 'cloister of trials' there. Except, this time, only step on the White Boxes in each room. Each boxs you step on plays a note or two from the Hym of the Fayth. Do you remember it? Well you better, because you have to recreate the tune. Its not too hard though. Once it is completed., the whole hym will play and you will be able to get the treasure from the 2nd room!

Now, return to Baaj and go to the unactivated alter. It will glow, and when that sequence is done, the symbol infront of the chamber will shatter. Now you can enter the room and pray to Anima, one of the most destructive Aeons of the game.