Team Rocket is the Main Antagonist Group found in Pokemon FireRed. As your trainer travels through the Kanto Region in search of Pokemon and Gym Badges, it will be up to you to stop Team Rocket from their heinous crimes. You will first meet these troublemakers in Mt. Moon, where they're trying to steal fossils. From there, you will have to defeat Team Rocket once more at the end of Nugget Bridge on Route 24 and then after they robbed a house in Cerulean City.
After obtaining your third Gym Badge and making it to Lavender Town, the story revolving around Team Rocket will begin to seriously take shape. They have recently killed a Marowak in Pokemon Tower, now holding Mr. Fuji captive at the top of the tower itself. Unfortunately, you won't be able to save Mr. Fuji until you defeat Team Rocket in their hideout found underneath the Celadon City Game Corner. It is here that you will meet and battle the Boss of Team Rocket, Giovanni, for the first time. After defeating him, you will receive an item that will ultimately help you defeat Team Rocket back in the Pokemon Tower in order to save Mr. Fuji.
Once Mr. Fuji is saved, you will next run into to Team Rocket in Saffron City. They have taken over the entire city, and are now causing trouble in the Silph Co. Building. Again, it will be up to you to travel through the skyscraper in order to find and defeat Giovanni once more, defeating all the Team Rocket Members standing in your way of doing so. After defeating Team Rocket in the Silph Co. Building, they will leave Saffron City and remain dormant for a while.
You won't run into Giovanni (not Team Rocket) until you have obtained the firsts even Gym Badges and return to Viridian City to take on the final Pokemon Gym. Believe it or not, Giovanni will turn out to be the final Kanto Gym Leader. Defeat him once more in order not to simply obtain the final Gym Badge, but also to have him verbally disband Team Rocket. It will appear Team Rocket is done now that their leader has left the group, but that won't stop some rouge Team Rocket Members just yet!
After defeating the Main Story and obtaining the National Pokedex, you will have to put an end to Team Rocket once and for all in the Post Game. This will begin by defeating them outside the entrance to Mt. Ember in order to obtain the Ruby, and then in Icefall Cave found on Four Island. You will defeat more Team Rocket Members on Five Isle Meadow within Five Island, but you won't be able to access their Warehouse on the same until you have learned the two password to it. Later on Six Island, you will find the Sapphire in the Dotted Hole, but a scientist to steal it right before you can grab it. Once this happens, you will finally be able to access the Rocket Warehouse on Five Island. Defeat Team Rocket with their Warehouse to obtain the Sapphire and put an end to their ways!