Caladbolg is a Celestial Weapon and it is the most powerful weapon for Tidus in the game.
You must obtain the Celestial Mirror before you can obtain or create any of the Celestial Weapons. Click on the link below for more information on how to obtain the Celestial Mirror:
In order to create the fully powered-up Caladbolg you will need to obtain the Caladbolg weapon itself first, then use the 
Sun Crest and the Sun Sigil to power it up.
You will first need to travel to the Calm Lands and complete the Chocobo Trainer side quest. Check out the following link for more information:
Once you have complete the Catcher Chocobo challenge make your way to the northwest section of the Calm Lands. There is a small pathway that leads downward that used to have a man blocking it. You can now touch the wall (which will only react if you have the Celestial Mirror in your inventory) to obtain Caladbolg.
Note that if you leave the Calm Lands the man blocking the pathway will re-appear. You will have to race the Chocobo trainer again in order to get him to move, but you won’t have to beat her this time.
Now you will need to power the Caladbolg weapon up. The only ability it has is 
No AP auto-ability. You must now obtain the Sun Crest and Sun Sigil in order to power it up.
Note: You may already have the Sun Crest if you had been following a guide previously. Check your inventory under the Key Items tab to make sure.
The Sun Crest can be obtained after you have defeated Yunalesca in the Zanarkand Ruins. Travel to Zanarkand and go all the way through, past the Cloister of Trials, and into the last room where you fought her. You can use the teleportation pads to warp there faster.
Walk down the stairs that lead downward. You will be teleported to the other set of stairs on the opposite side of the room. You must to this step in order to make a treasure chest appear at the back of the room. This treasure chest contains the Sun Crest.
If Dark Bahamut appears in this area you will have to defeat it first before you can obtain the Sun Sigil.
The Sun Sigil is a little bit more difficult to obtain. You must challenge the Chocobo Trainer to another race in the Chocobo Catcher challenge and you must obtain a time of less than 0:00 once you reach the finish line.
In order to do this you will have to obtain as many of the balloons as you can and make sure that you do not get hit by any of the birds.
The best strategy is to hit as many balloons as you can and accept that you will get hit by a bird or two. This challenge takes a lot of skill and a boat load of luck. Keep at it until you get it!
Return to Macalania Woods to the area where you received the Celestial Mirror once you have obtained both the Sun Crest and the Sun Sigil. Offer Caladbolg up twice to fully power it up using both the Crest and Sigil.
Caladbolg has the following abilities when fully powered up:
Break Damage Limit - Allows Tidus to do more than 9,999 damage in a single attack
Triple Overdrive - Charges Tidus’ Overdrive at triple the speed
Evade & Counter - Allows Tidus to counterattack physical attacks and gives the possibility of evading the damage as well. The counter will work regardless of whether the evade is successful.
Magic Counter - Allows Tidus to counterattack magic attacks
