Giratina is a powerful DRAGON/GHOST type that can be found deep in Turnback Cave, a place that is said to overlap a different, darker dimension...Anyway, Giratina can only be found and fought once in the game. Be sure to save. Also, Giratina can only be found after obtaining the National Dex and beating the Elite Four. Be sure that is done. Turnback Cave is found in a previously secluded place called Sendback Springs.

Make sure you have Rock Climb, and preferably Defog, because Turnback Cave is very foggy.

Bring many Dusk Balls, Ultra Balls, or a Master Ball if you were saving it to get a very strong pokemon. Also, if you don't want to fight lvl. 50 - 67 pokemon, grab some repels.

Fly to Veilstone City, if you aren't already there, then travel down the fence-maze area until you see a long, empty path stretching out to the right.

Go and travel that path until you come to a rocky wall by two trees standing together.

Use Rock Climb, and after the HM is done, you'll be at a large, clear lake, very much like Uxie, Azelf, and Mesprit's lakes. Go to the very farthest north by the lake. There will be another rocky wall at the edge of the lake.

Use Rock Climb again, and when the HM is done, you'll be standing next to a cave entrance. Go inside.

Congratulations, you have now entered Turnback Cave. Now for the trickiest part. There will be a rock wall ahead of you. Read the inscription.

There apparently no set ways to get to Giratina, but it is only accessible by passing three pillars before you pass 30 rooms. Once you pass the 3rd pillar, and room you enter from here on in will be Giratina's. Once you save before you face him, take notice of these things.

Giratina's moveset is:
Heal Block
Shadow Force
Earth Power
Slash

Giratina is level 70, so have a strong pokemon in your roster. After you catch it, which will most likely be a grueling experience, you can leave the cave. (not that you couldn't before). If you want, you can train on some powerful pokemon, (wild lvl. range gets boosted by ten after each pillar is passed) collect a rare item, an infinite amount of items will appear in Giratina's place after you either have caught it, or fainted it (rare bones, stardust) or you can take time to read this slightly ominous messsage engraves on the rock behind where Giratina used to stand.