Instructions
Travel to the city of Ecruteak and speak to the people in town to hear the story of how there was a fire in the town tower many years ago.
Head to the tower located in the upper right section of the town.
Enter the tower, then use the "Rock Smash" ability on the rock that is in the top of the room.
Defeat the trainer that challenges you after you smash the rock then continue down the hole in the floor. If your Pokemon were injured during the battle go back into town and heal them at the Pokecenter then return and go down the hole.
Walk towards the statues until they start to move and run out of the tower. The statues are the legendary Pokemon that have come to life, one of which is Entei.
Exit the tower and reorganize your party so that you have a fast Pokemon that has a blocking move starting battles. Because Entei is so fast and often flees as soon as battles begin, you want to have a Pokemon that blocks or disables Entei before he has a chance to flee. A Golbat that knows the "Mean Look" attack makes capturing Entei much easier.
Go to the Pokemart and buy "Repels" so that you don't get interrupted by ordinary Pokemon while hunting down Entei.
Save your game then exit the town and use one of the Repels. Walk through the clumps of grass outside of town to randomly encounter Entei.
Use a blocking ability like "Mean Look," "Hypnosis" or "Sleep" as soon as the battle begins. "Mean Look" works the best as the move prevents the enemy from escaping without wearing off.
Attack Entei until health drops down into the red, then capture it with a Pokeball. Use the best type of Pokeball you have in your backpack to increase the chances of capturing it. Your best chance is using Ultra Balls if you don't have a Master Ball to spare.