The best moves for giratina for me are shadow ball, shadow force, earth power (change it for aura sphere at lv 90) and outrage if possible, if not, stick with dragon claw till you can teach it with tha move tutors eiter outrage or draco meteor... If you prefer earhtquakerather than earth power you can teach it that with the TM.
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It depends on the level, its moves and its stats. But if even, it'll be Giratina
Ghost, Dragon, Dark, Fairy, and Ice type moves are Super Effective against Giratina
Feed best pokeblocks to your pokemon, Teach best moves for the contest your entering and just use the right moves at the right time.
His best moves are blizzard teach it to him hydro pump ice beam and (rain dance body slam or calm mind your choice) in my opinion.
Now, a Giratina surely needs Will-O-Wisp, really. A good nature is Quiet to improve his spec. attack and lower his speed. Giratina doesnt really need speed. Since Giratina's special attack is risen, learn him moves wich dont make contact with the other pokémon. Moves wich make contact are moves wich hit pokémon by using his, her or even its fists, feet,... e.g.: Earthquake, close combat,... Moves wich hit via spec.att dont make contact and are "launched" from the pokémon e.g.: Dragon pulse, T(under) wave,... My moveset: -Will-O-Wisp -Shadow Force -Draco Meteor The last move depends on how you use your Giratina. when he is Spec. Att user: Earth power. Lead: Shadow sneak, Ominus wind, ancient power. Bulky: Shadow claw, Aura sphere.