Articuno

• 1). Travel to the Seafoam Island. Be sure to take a Pokemon that knows Surf and Strength.
  
  
• 2). Complete the maze inside Seafoam Island. Articuno will be waiting at the end.
  
  
• 3). Start a battle with Articuno. Try to get its health as close to zero as possible. Start throwing Poke Balls at it until you have captured it.
  
  

Zapdos

• 1). Travel to Route 9 with a Pokemon that knows Surf.
  
  
• 2). Use Surf on the river along Route 9. Follow the river until you reach the Abandoned Power Plant.
  
  
• 3). Complete the maze inside the Abandoned Power Plant to reach Zapdos.
  
  
• 4). Engage Zapdos, lowering its health to as close to zero as possible. Toss Poke Balls at the legendary bird until you have captured it.
  
  

Moltres

• 1). Defeat the gym leader Blaine. Talk to Bill afterwards to receive the Tri pass.
  
  
• 2). Travel to Knot Island, also known as "One Island."
  
  
• 3). Travel through Mount Ember with a Pokemon that knows Strength.
  
  
• 4). Climb to the top of Mount Ember. Moltres will be in the center of the top level.
  
  
• 5). Engage Moltres and lower its health as close to zero as possible. Throw Poke Balls at Moltres until you have finally caught it.