Instructions
Go to the Goldenrod City Gym. Defeat all the Pokemon Trainers inside, and stand in front of the Gym Leader. Save your game, and challenge Whitney. Defeat her Level 18 Clefairy and Level 20 Miltank. Speak to the Pokemon Trainer nearby and talk to Whitney again, to receive the Plain Badge.
Enter the house surrounded with colorful plants to the east of the gym. Speak to the woman who is wearing red clothing. She will give you the SquirtBottle, which will go to the Key Items pocket of your Inventory.
Head east of the National Park to arrive on Route 36. Save your game, and stand on the square before the Sudowoodo. Press the "A" button, and the game will prompt you to use your SquirtBottle. Since the Sudowoodo doesn't like water, it will attack you.
Weaken the Sudowoodo with Fighting- or Water-type moves. Catch the Sudowoodo with a Great Ball, or knock it out. If you fail to capture or defeat it, reset "Pokemon Silver" and try again. This is the only Sudowoodo you will encounter in "Pokemon Silver."