Either cheat or "chain" 40 pokemon.
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The same way you would catch a normal Pokemon. The only difference is is that the Pokemon is shiny.
There are a few ways that you could get a shiny Deoxys in Pokemon Platinum. One way would be to get someone who has hacked one to trade.
Yes the same way you get shiny Pokemon in the other Pokemon games is how you get shiny Pokemon in heartgold. There is a free shiny Pokemon in the lake of rage.
To get a shiny teddiursa would be brilliant. It is very hard to find. The best way to get a shiny is through chaining. You need to beat the Elite 4 and get PokeRadar.
No. But once i fought a wild shiny zubat in a cave on the water. And my brother fought a wild shiny Raticate above the fight area (route 225)