First, you have to know where to catch a Hoothoot/Noctowl. Hoothoot appears on Route 205 North, Route 210, Route 211 West, Eterna Forest, and in the Great Marsh at night. Noctowl appears in all of those places but Route 205 North.
Next, you can either try your luck (since shinies have a 1/8192 chance of appearing) or use the PokeRadar and chain Hoothoot/Noctowl to increase the chance of getting a shiny to 1/200!
You can also use the Masuda Method and breed two Pokemon from foreign countries to increase the chance of getting a shiny fivefold, up to about 1/1638.
And, you can always hack to get a shiny. But what's the fun in that?
Here is a guide to chaining (it is the same in D/P as in Plat).