After you get a parcel from a Poké Mart clerk in Viridian City, you return to Pallet Town to deliver it to Professor Oak.
Deliver the Parcel
Go south from Viridian City to Pallet Town, jumping down the ledges in Route 1 to get there more quickly. Go into the lab and talk to Professor Oak. He will give you and your rival some Razz Berries.
Battle Your Rival
When you try to leave the lab, your rival will challenge you to a pokémon battle. If you have Pikachu, you will battle your rival's Eevee. If you have Eevee, you will battle your rival's Pikachu.
You can change Pokémon during the battle. To fight, choose Fight, then choose the move that you want to use. You can choose Bag to use items from your bag.
After you win the battle, all pokémon in your party will get EXP. You get 120 Pokédollars for winning.
Communicate
After your battle with your rival, your menu will have the Communicate option unlocked. You can use the Mystery Gift option to check for gift distributions from the Internet or gift codes, or you can choose Play With Others to trade or battle with other players.
At this point, your partner pokémon will ride around on you, so you can choose another pokémon from your party to take out of its pokéball. You can't have your partner pokémon follow you anymore.
You can also get Mew from your Poké Ball Plus now, if you have one.
Play With Your Starter Pokémon
Go north from Pallet Town and you will find your rival's sister, who gives you some Sportswear. Afterward, you can pet your pokémon and feed it berries. Follow the on screen instructions to do so. You can go to the menu and choose the Play With Pikachu or Play with Eevee option any time.
To dress up your pokémon, use the Clothes Trunk in your bag.
Back to Viridian City
Go north from Pallet Town. In Route 1, you will find the Poké Mart clerk who gave you the Parcel earlier. Talk to him to get a free Potion.
Farther north, the kid in the blue hat will challenge you. Youngster Ronny has a level 3 Rattata. You get 60 Pokédollars for winning, and 3 Poké Balls.
Back in Viridian City, you will find your rival, who recommends healing your pokémon at the nearby Pokémon Center. Just talk to the nurse behind the counter to heal your pokémon.
Route 2
The Pokémon Gym in Viridian City is closed right now, but the path to the north is no longer blocked, so just go north to Route 2 for now. Some of the pokémon that you can catch in Route 2 are Weedle, Rattata, and Pidgey.
Your next destination is Viridian Forest.