I've been hunting the friggin things since Christmas. I can't be doing it right. I've just been standing in front of the Poké Balls with the starters in them, and soft resetting when they aren't shiny. Am I doing this right?
Here's a step by step process.
Save your game directly in front of the Poke Ball machine. This will be your reset point.
Hit A and look at your selection of starters. You can scroll through them to see all 3. If one of them is shiny, they will appear shiny from this view, but it is up to you to find it, the game gives you no other hints that the Pokemon is shiny. I recommend researching Chikorita, Cyndaquil, and Totodile's shinies so you know exactly what they look like.
If there is no shiny, soft reset. On a 3DS console, this can be done by pressing L, R, and Select/Start at the same time, or if on a DS, by pressing L, R, Start, and Select. This resets the game faster than closing the game/turning your system off every time inbetween encounters.
That's it! Soft reset hunts are pretty simple, however they tend to have a lower odds of finding your Shiny Pokemon. In this case, the odds are 1/2730, because you are seeing three different Pokemon in one encounter. Even if you get two encounters a minute, you are only encountering about 120 Pokemon an hour, and to reach odds, will still take about 23 hours. This does not mean your guaranteed one at 23 hours, or at 46 hours, or 92 hours. It's still an obscenely low occurrence.
Hope I could help!