Second Gym to Third Gym
When you exit the gym, go west. Find the boy who lost his farfetch'd. You will see a farfetch'd somewhere near that place. Chase the bird until it goes right in front of its trainer. This boy will reward you will HM01 and you could teach cut to one of your pokemon. You will see a tree right above the trainer. Cut it down and go north. You will see one of those buildings that separates routes. Inside, talk to the girl with the butterfree and she will give you a TM.
Kept on going north. You will see a house with a pond in front. You could find a krabby in their pond. The people in the house could breed your pokemon. Go north and fight the trainers until you get to the town.
This town is large. Go find one of the houses with a staircase that goes to the basement. There are trainers to fight and you will see a little path to a blue door. It is locked right now but remember it. After you beat other gyms, you will have to come back and fight the Team rockets. When you finished fighting the trainers, go up the other staircase. You will be in another house. Go to the tall metal building and talk to the woman furthest on the right. She will ask you a couple of questions. You already know the top is "yes" and the bottom is "no". So answer yes, yes,yes,no,yes,no. She will give you a radio. Go up the stairs, and you will see a woman and a jigglypuff. Go to the left side of the room and you will see a person blocking the other staircase. It is not important that you get him out of the way right now, so forget about him. But DO remember, you will have to come back to this metal building later. There is a house on the bottom right of town. Talk to the person inside and you will get a bike. Go to the house right of the gym. There, you will see two girls. Talk to both of them. One of them will give you "Squirtle Water" You will need that later.
Now go inside the gym, fight all the trainers until you get to the gym leader. This gym uses normal type pokemon. The gym leader has a Clefable and a Mirutanku. It looks like a stupid cow but it not very easy to beat.