Legendaries Pokemon Platinum

Giratina
You catch Giratina in the Distortion World.

Uxie, Mesprit, Azelf
After you finish the Distortion World talk to Professor Rowan and then you can catch them at their lakes. Uxie will be at Lake Acuity, Azelf at Lake Valor, and Mesprit will be at lake Verity. Once you see Mesprit at its lake it will start to wander around Sinnoh so you must run into it in the wild to catch it.

Dialga and Palka
To obtain these Pokemon you will need the Adamant and Lustrous Orbs from Mt. Coronet. Now go talk to the women in the big house in Celestic Town. Now go to the top of Spear Pillar and you will be able to battle and catch them.

Moltres, Articuno, and Zapdos
Talk to Professor Oak in Pal Park. Now visit him in Eterna City to get the Up-Grade. Now you will be able to catch the birds as you encounter them around Sinnoh.

Heatran
To get Heatran go to the Survival Area in Stark Mountain and speak to Buck. Now talk to him again in the Trainer Cafe. Now go back to Stark Mountain to battle it.