Here's how it works:
1. Start the game: When you begin Pokemon Crystal, you'll meet Professor Elm at his lab.
2. Choose your starter: He'll give you three Poké Balls, each containing one of the starters. You get to pick the one you want.
3. No catching needed: Professor Elm gives you the starter you choose, so you don't have to catch it like you would with other Pokemon.
You'll have the chance to encounter the other two starter Pokemon in the game later on, but you won't be able to catch them. They will be used by other trainers, and you'll need to defeat them in battle to gain their respect and possibly add them to your team.