A listing of the friends you will meet in the game, and how to deal with them.

You
There's not much to say. You are the main character in the game. You can name yourself whatever you want, but one of the default names for your character is Ash.

Professor Oak
He wants to help you in your quest to become a Pokémon Master...or does he? It's strange, but Professor Oak seems more concerned with his goals than yours. If that means helping you, he'll do it.
Professor Oak will give you your first Pokémon, and a little later, your Pokédex. If you don't get the Pokédex, you won't be able to continue past Viridian City.
Professor Oak will also rate your Pokédex from any of the PCs in any of the Pokémon Centers.

Professor Oak's Aides
They'll show up throughout the game, and if you've collected a certain number of Pokémon, they'll give you an item. The first item you get is the Flash TM. When you've collected 30 Pokémon, you can get an Itemfinder, used to (you guessed it) find items. Later on in the game, one of Professor Oak's aides will give you Exp. All, which shares experience points with all 6 of your Pokémon. It's not really worth it to me, but you'll have to see if you like it.

Fishing Guru
This guy, who lives in Vermillion City, will give you a fishing rod if you say you like fishing. His brothers, who appear later on in the game, will give you better rods that can catch more Pokémon.

Traders
You'll meet up with some people in the game who will offer to trade with you. Usually they have rare Pokémon, and want common ones in return.

Nurse
I can't call her Nurse Joy because she technically doesn't have a name, but that's who she is. She works at evey Pokémon Center in the game, and will heal your Pokémon for you.