Instructions
Go to the right (east) side of Jubilife City and enter route 203. Keep walking to the right until you see a kid with a hat and red shirt.
Follow the path of grass (on foot) on the left of the kid. Use the PokeRadar while standing in the grass and pace back and forth. Keep the PokeRadar active until you encounter Ratls (which may take a while, as there are Starly and Shinx Pokemon in the grass also).
Use a grass, water or fire type Pokemon to weaken Ralts. Because Ralts is a low level Pokemon found at the very beginning of the game, your starter Pokemon or any Pokemon you've captured and level up to at least level 5 will be more than sufficient.
Use a standard PokeBall to capture Ralts after he has 28 hit points or less. Ralts puts up very little fight, so using a more stronger ball (such as an Ultraball) would be a waste.