Once you've delivered Oak's Parcel at the Viridian City Pokémon Mart, the clerk will give you a Poké Ball and a Potion as a thank you. He'll also inform you that Professor Oak is looking for you back in Pallet Town. This is your cue to return home.
Upon re-entering Professor Oak's Lab, he'll be delighted that you delivered the parcel. He'll then entrust you with the Pokédex, a high-tech encyclopedia designed to record data on all Pokémon. He'll also give you five Poké Balls, allowing you to start catching your own Pokémon! Blue will also receive a Pokédex, setting up your rivalry to 'catch 'em all'.