Catching a shiny Pokemon is the same as catching a non-shiny Pokemon. You just need to lower its health and use a Pokeball to catch it.
However, to find one in the first place is very hard to do. You can either rely on the RNG and hope to encounter one randomly, or you could trade for one using the internet or with any accomplices you may know. You could also try to breed one from the daycare as well.
Chat with our AI personalities
First you need to catch a shiny scrotum then level it up to level 50 and it evolves into a shiny rotom.
...shiny Pokemon are always shiny... ._.
The same way you would catch a normal Pokemon. The only difference is is that the Pokemon is shiny.
On Action Replay press disable Shiny Pokemon.
It takes luck to come across a shiny, but when you find one you catch it like you would catch a regular Pokemon.