You need to have obtained Surf from the woman in Celestic Town.
The gym leader of Hearthome City is Fantina. When the player first arrives at the city, she will not be in her gym. She can only be battled after the player deliver the Old Charm to the elder at Celestic Town.
The 6 gym leader in at Canalave City. the gym after the hearthome City gym!!!!!
hearthome
after you beat the 4 gym leader in hearthome city
Surf
She is in Hearthome City.
the gym leader has it
go to hearthome city and fight the gym leader there
just beat the fourth gym leader
The fifth gym leader is fantina.She is in hearthome city.
you beat the gym leader
The third gym leader is in Hearthome City. But i think the gym leader says that you are not ready yet. (don't remember) you have to beat Pastoria and Veilstone's Gym leader first and then you can battle Hearthome's leader.