As your looking at the calm-lands, its on the far left (at the edge looking down into the ravine). Its probably best to go to the corner farthest from the exit out of the calmlands (the exit that leads to mount gagazet). Start in that corner, and work your way along the edge of the ravine, towards mount gagazet, until you come to a little passage that leads down.

There is a man there, who won't let you down there. In order to get him to move you have to compete in the chocobo race to distract him. That's not all, you have to get a time of 0.0 seconds in the chocobo race (which will take some time to achieve), and as soon as you win the race, run directly to the passage, and the man will be gone, distracted by the race. I think 2 components make up the ultimate weapon, one you get for getting a time of 0.0 seconds in the chocobo race, and the other is in a chest in the cliff in the passage the man was guarding.

If its still unclear, try this website:

http://www.bellaonline.com/gaming/st...b_ffxwalk.html

- there's a FFX walkthrough here, with the method of getting all ultimate weapons, and a map of where to find Tidus' weapon, as I described above.