Walkthrough:Pokémon Yellow/Part 2

Under construction With Oak's Parcel, go down Route 1. Use the ledges to avoid wild Pokémon attacks, or go in the grass and train your Pikachu. Once you arrive in Pallet, go to the lab and talk to Oak. He'll thank you before your rival comes in. Now that you're both there, Oak gives you the Pokédex. The PokéDex is a encylopedia of Pokémon that you fill in. Catch Pokémon, and its Pokédex entry will be filled.

Your rival will then gloat that he'll fill in the Pokédex first. He'll also get a map before you from your rival's sister, and he'll leave. Go ahead and leave and head to your rival's home. Get the Map from the girl on the table, and head back to Viridian City. If you want, head left towards Kanto Route 22. Else, go north.

Route 22
This is the entrance to the Pokémon League. We won't be going here for a while, but there's a thing here we want.

Continue on the route until you see your rival. He has another weapon—Spearow. The Eevee remains Eevee, but, as said in the last part, this battle will change Eevee's evolution. See here for more.