if you're very lucky, you can encounter it, but I'm not sure about its catch rate...
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All I remember is that he caught a shiny noctowl, if you consider that rare Ash also catches Snorlax
Snorlax can be shiny. All known Pokémon can be shiny actually. Normal Snorlax has a eggshell white and green body color while shiny Snorlax has a eggshell white and deep blue body color. Now, if you plan on hunting one then use FR/LG. Those games have 2 obtainable Snorlaxes. :]
The same way you would catch a normal Pokemon. The only difference is is that the Pokemon is shiny.
It takes luck to come across a shiny, but when you find one you catch it like you would catch a regular Pokemon.
No they programmed the game so you can't catch shiny victini, reshiram, and zekrom. All other pokemon can be found shiny.