Alright. Next, you have to go to Olivine City. Take the left exit out of Ecruteak City. The route is pretty straightforward; it shouldn't be too hard. After doing so, go to the Lighthouse. Go all the up to the top floor. Jasmine (6th gym leader) will be there with a sick Ampharos. She'll ask you for help. Go southwest, and Surf down and left to reach Cianwood City. There you can beat Chuck, Fighting type gym leader. Beat him and get the Storm Badge. Exit the gym, and Chuck's wife will give you HM Fly. In one of the houses, a man will give you medicine for Ampharos. Fly/Surf back to Olivine, give Jasmine the medicine, and she'll go back to the gym. Battle her and her steel types for the Mineral Badge.
HM Surf can be found in the Ecruteak Dance Theater after beating the Kimono Girls. A man in the audience will give it to you when you speak to him.