Step 1: Choose which Shiny Pokemon you want
Pretty much any wild Pokemon that appears in grassy areas is a candidate for Shiny hunting, but some are easier to find than others. When you're first starting out, we recommend that you try for a "swarm" Pokemon, as these seem to be the easiest to chain using the Poke Radar. Once you've obtained the National Dex, talk to Lucas's/Dawn's sister in Sandgem Town and she'll tell you which Pokemon is swarming that day and where to find it.
Step 2: Find a good place to start chaining
You'll want to find as large a grassy spot as possible, preferably one that covers most of the screen. It's also a good idea to chain in an area without weather effects like rain, snow, or sandstorm, because this can make it difficult to see which patches of grass wiggle when you use the Poke Radar.
Above: We found this Shiny Shinx in this large grassy patch just north of Sandgem Town on Route 202