According to legends in the town, the yawn of a Slowpoke causes rain. 400 years ago, a drought in Azalea Town ended right when a Slowpoke yawned. This caused Slowpoke to be highly revered by the townspeople.
Before entering the well, you must visit Kurt, who'll explain that Team Rocket is trying to gather Slowpoke tails to sell for large amounts of money. He'll then storm off to do something about it in a fit of rage. Follow him to the well, and the person that was guarding the well when you entered the city, will be gone. Upon entering the well, you'll run into Kurt, and he'll tell you that he pushed the guard out of the way, but fell into the well in the process, as well as hurt his back. He asks you to finish the job by clearing out Team Rocket.
The lower floor can only be accessed after the player has acquired both Surf and Strength. This section of the well enters from the ladder in the middle of the cave, on an island in an underground lake. By surfing around this floor, there is a man on an island who will give players a King's Rock if they talk to him, while TM18 (Rain Dance) can be found on the ground.
Kurt will make Poké Balls out of Apricorns after you've taken care of Team Rocket. If you bring him an Apricorn, he'll take it and have you come back the next day to pick up your new Poké Ball. The Poké Ball you get depends on the Apricorn you drop off. Apricorns can only be obtained from Apricorn trees located in special locations in Johto and Kanto. A tree holding White Apricorns can be found right outside Kurt's house.
Azalea Gym
If you started with Cyndaquil, then you're in luck. Every Pokémon in this gym has a Fire-type weakness that can easily be exploited. If not, then try raising Onix above level 9 so it can get the move Rock Smash, which will be super effective against the Bug-Type Pokémon of this gym.
After Leader Bugsy is defeated, he will give the player the Hive Badge, which allows you to use HM01 Cut outside of battle and control Pokémon from trades up to level 30, as well as TM89 (U-turn).