1. Beat the first gym: The first gym is in Violet City, and you need to beat the gym leader, Falkner, to progress.
2. Travel to the next town: After beating Falkner, you can travel to the next town, Azalea Town.
3. Investigate the strange noises: Once in Azalea Town, you'll notice strange noises coming from the nearby forest.
4. Clear the forest: You'll need to battle your way through the Ilex Forest to reach the town of Ecruteak City.
5. Solve the Ilex Forest mystery: There are three main areas in the Ilex Forest with each having their own issues you'll need to solve, including finding a lost girl and a Pokemon's egg.
6. Enter the next town: Once you solve the mystery of the Ilex Forest, you'll be able to enter Ecruteak City, where the second gym is located.
Important Note: The second gym is located in Ecruteak City, not Azalea Town. Azalea Town is the town you visit immediately after Violet City.