In Professor Oak’s Lab, talk to Professor Oak and he’ll ask how your Pikachu or Eevee are doing. At that point, if you have Pikachu, it will climb up onto your shoulders, and if you Eevee, it will hop up onto your hat.
You’ll then give Professor Oak the Parcel and, shortly afterwards, your rival Trace will show up. After a bit of dialogue, Oak will give you and Trace some Razz Berries, which can be used to make Pokémon easier to catch.
As you try to exit the lab, Trace will stop you and challenge you to a Trainer Battle, which will be your first one of the game.
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While in a Trainer Battle, you’ll be able to fight using the Pokémon you’ve caught. You can choose the Fight command and then pick one of your active Pokémon’s moves to use for that turn. You’ll always lead with the Pokémon that’s in the first position of your party — the top-left slot — although you can swap out your Pokémon by selecting Pokémon in battle. Keep in mind that doing so uses up your turn, so whichever Pokémon you send out will likely take a hit during that turn. You can also use items from your Bag to heal your party, even your Pokémon that aren’t active on the field.
This fight should be easy if you’ve caught a few Pokémon. Your partner Pokémon should have no difficulty at all taking down the foe if you use Tackle, Thunder Shock, or Quick Attack. The type of the move you use may be super-effective against some Pokémon, causing them to take double-damage, or it may be not very effective against others, where it does only half. For this fight, that will not be an issue, though.
Also keep in mind that if you are not able to hit for super-effective damage, you should always try to use moves that are of the same type as the user — this grants the Same Type Attack Bonus, or STAB for short, which adds an extra 50% to the attack’s damage. So if you started with Pikachu, you’ll want to prioritize using Electric-type moves like Thunder Shock instead of Quick Attack, unless another move is super-effective or has an effect you’d benefit from.
After each Trainer Battle, you’ll receive Prize Money — also known throughout the community as Poké Dollars — which is the currency used throughout the Pokémon world to buy items.
Now that you’ve beaten Trace, he’ll run off and you’ll be free to return to Viridian City. At this point the Communicate option is unlocked on your menu, which allows you to trade and battle with other players.
As you leave Pallet Town, though, be sure to talk to Trace’s sister near the entrance to Route 1. She’ll give you the Sportswear clothing item for your Pikachu or Eevee. After that, your Pikachu or Eevee will hop down onto your arm and allow you to interact with it.
From here, choose Partner Play and you will be able to pet your partner Pokémon. You can either use the Joy-Con or Poké Ball Plus to do so if you’re playing with the Nintendo Switch docked, but if you’re playing in handheld mode, you can use the touch screen to pet your Pikachu or Eevee instead. You can poke its ears, its tail, its nose, and also its belly or chest. You can also feed your Pokémon a berry to raise its happiness.
This unlocks the Play with Pikachu or Play with Eevee option from the main menu, which will bring you back to that screen in the future. It’s a nice thing to do from time to time, but there are also additional features that will be unlocked later.
Don’t forget to go to the Clothing Trunk in your Bag and dress your Pikachu or Eevee up with some Sportswear! It’s purely cosmetic and offers no advantage, so you don’t have to do this, but it can be cute seeing your partner Pokémon dressed up like you.