Well, you can also breed to get them, but you have the same odds of obtaining a Shiny from an egg as you do seeing it in the Grass.
If you ever, ever, ever, EVER encounter a Pokemon of an unusual color, or a Pokemon that you see stars shoot out of, CATCH IT, IT'S SHINY.
Duh.
Also, if you don't know what the term "EV Training" means, then you probably shouldn't train the Shiny until you learn about EV's.
That's about it. Shiny Pokemon are no more powerful than their normal counterparts, but a few look cooler, and you can usually trade them for something pretty good.
One last thing: Always make sure you have Pokeballs. I've caught one Shiny in my life. It was a Wurmple that just popped up in Eterna Forest. I had TWO Pokeballs left. Fortunately, I was able to catch it, but it was a rather close call, and pretty scary.
Hope I've helped.