Instructions
Play the game until you receive the National Pokedex. You will receive it from Professor Oak just before you board the ferry in Olivine City for the first time.
Buy some Poke Balls at a store in the town nearest to the location where you want to search for Chingling. Look for low level Chingling in the Dark Cave or Diglett's Cave. Look for higher level Chingling in the Cerulean Cave or Ice Path. You can also find Chingling in the Union Cave, Whirl Islands, Victory Road, Mt. Mortar, Mt. Silver and Mt. Moon.
Wait for Thursday and enter one of the areas where Chingling dwells. Open your Pokegear and tune into the Sinnoh Sounds radio channel. After walking around with the music playing, you will randomly encounter a Chingling.
Battle the Chingling until its health bar is in the red, and then throw a Poke Ball to capture it. Chingling is a Psychic-type Pokemon, with Psychic-type weaknesses. As such, it is vulnerable to Bug and Ghost-type Pokemon, so you run the risk of knocking it out if you fight it with these types of Pokemon.