Instructions
Head west on Route 39 toward Olivine City; Olivine is the home of the Olivine Lighthouse.
Enter Olivine City; your rival will appear and tell you that the Gym Leader, Jasmine, is at the Lighthouse and not at the gym; she is tending to a sick Pokemon there. Head east to go to the Olivine Lighthouse.
Head up to the top floor of the Lighthouse, battling the Trainers you confront along the way. When you arrive at the top, approach Jasmine and the sick Pokemon. She explains that Ampharos, or Amphy as the Pokemon is nicknamed, gives light to the Lighthouse and has fallen ill. Amphy needs a special kind of medicine from Cianwood City.
Head south out of Olivine City and use the HM move "Surf" to go south to Cianwood City. Go to the Cianwood Pharmacy and speak to the proprietor; once you tell him that the Ampharos is sick, he will give you the "Special Medicine." Surf back to Olivine and go back to the Lighthouse. Jasmine will administer the medicine to Amphy, who will immediately recover.