Location: New Bark Town

Method:
Naturally, the first Pokémon you obtain is the starter Pokémon. Like in all games, once you have chosen your starter, your rival will pick the Pokémon that is super effective against yours

Location: Goldenrod City

Method:
The first gift Pokemon you are likely to encounter is in the form of a carrier pidgeon Spearow. The Pokemon's trainer is encountered on Route 35 and the destination is Route 31. Spearow comes holding mail which you can simply transfer to another Pokemon if you wish to keep the tiny bird Pokemon. Upon delivery of the mail, you will receive TM50 Nightmare.

Location: Goldenrod City

Method:
After meeting Bill in Ecruteak City, head back to Goldenrod City and find his house. Along with getting a phone number for the PC from his sister, you can pick up an Eevee of his for free. The Eevee comes at Level 20 and is Normal-type so it'll be useful against the Ecruteak Gym when it learns Bite or Mud-Slap. Although it has five evolutions, Espeon or Umbreon are the ones you'll be most likely to see because of the rarity of evolutionary stones in these game. Both are also excellent for the Ecruteak Gym.

Location: Violet City

Method:
The egg that you had at the beginning of the game will be given back to you after beating Falkner, should you go to the Violet City Pokemon Center. The egg should hatch into Togepi by the time you reach Goldenrod City. Togepi doesn't know any attacking moves when it hatches so you'll have to baby it for a while before using it in battle. However, upon evolution it gains a formidable Special Defense and decent Special Attack stat in Togetic.

Location: Cianwood City

Method:
After having all of his Pokemon stolen by your rival, a guy in Cianwood City will entrust to you his Level 15 Shuckle for safekeeping. The mold Pokemon can only be acquired through Rock Smash in Cianwood City and Vermilion City otherwise so it may be worth your while to pick this one up. Although its defenses are stellar, it has pitiful Attack and Special Attack and learns very few useful moves. An interesting quirk is that giving Shuckle a Berry will create Berry Juice some time after, and a Rare Candy even longer after that. Mania will want his Shuckle back after you keep it for a while, though it is up to you whether you want to give it back or not.

Location: Mt. Mortar

Method:
Deep inside Mt. Mortar lies the Karate King. He will challenge you to a battle with a Level 34 Hitmonchan and Level 34 Hitmonlee. This battle is very similar to the one in Red and Blue against him so whatever tactics you used against him then will work here. Upon defeat he will give you a Level 10 Tyrogue, which can evolve into Hitmonchan, Hitmonlee, or Hitmontop depending on its stats. You must have less than six Pokemon in your party to get Tyrogue will will need to climb the Waterfall in the middle Mt. Mortar entrance to meet the Karate King.