First of all, you'll need to obtain the 7 Gym Badges...
To get there, you must first have beaten the Canalave Gym, which triggers the Canalave Library event. After it, you must go to all three lakes and defeat each Team Galactic Commander there. Before you can go to Lake Acuity, you must beat the Snowpoint Gym.
after you help your rival at lake acuity you go back to galactic headquarters in veilstone and the storage key will be held by a grunt out side the building. you have to talk to him so he can drop it in front of you before leaving. it opens the lock in the warehouse on the other side of the city.Next, head to the Veilstone Team Galactic HQ and make your way through until you reach Cyrus. Defeat him, then head to Mt. Coronet from either the Oreburgh or Hearthome side. Make your way through(its long), then defeat everyone at the top of Spear Pillar(the top of Mt. Coronet.) Save your game, then step up and battle Palkia!
When catching, do NOT use a Masterball. The catch rate of this Pokemon is high for legendary Pokemon. Instead weaken with an attack and then chuck quick balls. Because quick balls lose their effectiveness after 5 turns, switch to ultra balls. You probably won't even need the ultra balls if it takes only one hit to get Palkia down to red.
if you have anymore questions about this you can ask me on the chat,
hope I helped