Surf east of Route 42 (east of Ecruteak City) to reach Mahogany Town. There, go north to reach the Lake of Rage, capture the Red Gyarados, go back to Mahogany Town to Team Rocket's hideout (hidden inside of a shop), then face Pryce, the town's gym leader, after completing the hideout. He uses Ice-type Pokemon.
A good tip for when you're heading to the Lake of Rage: be sure to take the path left of the gate to avoid having to pay Team Rocket a P1,000 toll.
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In Cianwood City you receive the medicine from the medicine shop. To give the medicine to the gym leader you have to go to the top of the lighthouse in olivine, which is where she will be. She will then return to her gym where she will battle you. Be careful - her Pokemon (2 magnemites and a Steelix) can be tough! Good luck! :)
you go to olivine then battle jasmine
you go back to olivine
It is on Cianwood City Island. You have to surf there from Olivine City. (NOTE: the gym in Olivine is actually the 6th Gym battle so go to Cianwood Gym first) Before you go to Cianwood City make sure you visit the Olivine lighthouse top floor to talk to the Olivine Gym Leader about a sick Pokemon first.
It's in Cianwood City. You have to go to Olivine, then surf & cross the sea to reach it.