Instructions
Speak with Professor Elm in the Pokemon Laboratory. He will offer to give you a starter Pokemon to accompany you on your journey.
Select the Pokemon you want and press "A" to confirm. You will then receive the Pokemon.
Press "Start" to bring up the in-game menu. Select "Pokemon" and view your starter Pokemon's information. If it is a different color than normal and has a yellow star to the right of its sprite, your starter Pokemon is shiny.