Instructions
Go to Goldenrod City, which is north on Route 34 and south on Route 35.
Enter the flower shop. It's located in the northeast corner of town.
Speak with the woman inside. She'll give you the Squirt Bottle.
Go to Route 36. It's north of Goldenrod City.
Continue down the forest path until you encounter the Sudowoodo. Use the Squirt Bottle on it to initiate the fight.
Attack the Sudowoodo until its health bar is yellow or red. Once it's weakened, throw pokeballs at it to try to catch it. If you don't want to catch it, continue attacking it until it dies. When the battle is over, the Sudowoodo will be gone and you'll be able to proceed.