It depends on the game version.
RED - BLUE - YELLOW
You need to first get CUT from the SS. Anne then use cut to cut the bush blocking the path to the gym. Upon entering, you will notice trash cans. Look in the cans and when it says "the 1st switch has opened" look in one of the adjacent cans for the second switch. If they reset, don't worry. The 2nd switch will always be next to the 1st.
GOLD - SILVER - CRYSTAL
Olivine city, top right of the map is the gym.
RUBY - SAPPHIRE - EMERALD
Upon entering Wattson's gym, you will notice electric force fields on the map. You will also notice thunderbolt switched. Upon stepping on the two switches, the electricity will shift opening up the area where Wattson is.
DIAMOND - PEARL - PLATINUM
You get the third badge (Cobble Badge) in Vielstone city. The gym is located in the southwest area of the town, north of where you got the coin case.
Chat with our AI personalities
the third badge in sapphire is at mauville city(north of slateport city)
Head to lavaridge town for your next badge.
Its hard to say -.-
Go North to Mauville City
After you beat the gym, you must leave, heal ur pokemon, then go back and talk to the leader and she should give you the badge