Instructions
Go to Cerulean City and walk to the right until you leave the city and enter Route 10. You eventually come to a Pokemon Center situated next to a river.
Face the river by the Pokemon Center, and press "A" to surf on the water. Head down and get out of the water when you see a building appear.
Enter the building. This is the Power Plant. Speak to the manager, who informs you of the missing Machine Part. Leave the Power Plant and go back to Cerulean City.
Walk up to the Gym in the center of town. A Team Rocket member will run into you and talk about a part that he has hidden. Follow him north, trapping him on the bridge.
Talk to the Rocket member to battle him. Once you win, he tells you that the Machine Part is stashed inside the Gym.
Go into the Gym, and walk to the upper-left corner of the small square of water. Press "A" to recover the Machine Part.
Surf back to the Power Plant and talk to the manager again to return the Machine Part. This completes the side quest.