Location: Mt. Moon

Method:
The first place you'll see these troublemakers is in Mt. Moon, where they're trying to steal fossils to sell. They mostly use weak Pokemon like Zubat and Rattata.

Location: Cerulean City

Method:
Two Rockets exist in Cerulean City. One is at the top of Nugget Bridge trying to make an offer you can't refuse, and the other has stolen a TM you'll need to retrieve at the house above Cerulean Gym (the former being only accessible after being said Gym). You'll get TM28 Dig for your troubles as well as passage to Vermilion City. The first Rocket uses Ekans and the second Drowzee, both troublesome in their own right.

More Rocket Grunts are in the areas surrounding Cerulean City. The first has set up a recruitment regiment on Nugget Bridge, and the other is hiding out in the backyard of the house he just robbed (after Misty is defeated). You will have to defeat both if you want to ride the S.S. Anne in Vermilion City..

Location: Celadon City

Method:
Celadon City has been overrun by Team Rocket with suspicious activity being linked to the Rocket Game Corner. Inside, a Rocket Grunt is idling by a poster on the back wall. Defeat him and you will be granted access to their secret hideout in the basement. Navigate the maze of warp panels on each floor, but be careful as they'll force you to move in one direction. You'll need to find the Lift Key on B4F to ride the elevator down on B3F to the Rocket Boss Giovanni's private office. There, you can fight him for the first time. If you defeat him, you receive the Silph Scope, which allows you to identify Ghost-type Pokemon.

The Rocket leader Giovanni fights with a fairly simple team the first time. All three of his monsters can be defeated with Fighting-type moves.

Location: Pokémon Tower

Method:
The Rockets killed a Cubone's mother in the Pokemon Tower and took Mr. Fuji hostage. Before you can get to the top floor, you must calm the angry ghost of the mother Marowak by defeating it in battle. You can't catch this Pokemon.After that, defeat the three Rockets and talk to Mr. Fuji to receive the Poke Flute..

Location: Saffron City

Method:
Saffron City is taken over by the Rockets, who block entry to homes as well as the local Pokemon Gym. After you beat Koga, the guard at Silph Co.'s office building will drift to sleep and you can enter to find Team Rocket staging a hostile takeover. To make things easy, head for the 5th level right away and get the Card Key at the bottom. From here you can open every door in the building and can avoid the pesky warp portals that will take you god knows where in the building. Take this to the 3rd floor and open the room on the center-left, taking the warp portal on the far left to gain access to a second warp portal that'll let you meet up with your rival on floor 7. After facing him, you'll have free access to a portal taking you to the president's room. Giovanni demands he turn over the Master Ball, which guarantees any Pokemon can be captured.

For the Rocket matches, many can be skipped. If you're a completionist though, be warned that they use Pokemon they haven't tried before. Magnemites, Cubones, and Voltorbs are used as well as Koffing, Raticate, and Golbat. Weezing, Arbok, Electrode, and Marowak might be hard to fight, so remember to open and use the healing room on floor 9 whenever you need to.

Giovanni's team is a bit more diverse, including Nidoqueen and Kangaskhan. After you defeat him, collect the last of the seven badges then go to Viridian City, where Giovanni has resumed his post as Gym Leader.

Location: Viridian City

Method:
Although the gym itself is not populated with Team Rocket members, this is the last place you meet Giovanni. He uses a team more centered around Ground-types, and you will receive the final badge along with other rewards once he's defeated. After the match he announces that he will be abandoning Team Rocket for good to dedicate himself to training. However, his team sees otherwise...which you will find out after beating the Pokemon League!

Location: Mt. Ember

Method:
Once you become Champion and acquire the National Dex, go to One Island to visit Celio. He will send on an errand to collect the Ruby that lays hidden in Mt. Ember. Unfortunately, some rogue Team Rocket members are also searching for it and will ambush you. Defeat them and find the Ruby inside. One of the grunts will even give the first password to their secret hideout on Five Island. Take the Ruby to Celio for your next instructions.

Location: Four Island

Method:
After Celio gives you the Rainbow Pass, take a trip to Four Island, home of the Elite Four member Lorelei. Find her in the Icefall Cave, where Rocket members are harassing local wild Pokemon. After you defeat them, Lorelei will thank you while the members flee to their base on Five Island.

Location: Five Island

Method:
The Rocket Warehouse was constructed in Five Island Meadow and remains their stronghold for the rest of the Sevii Islands arc. However, you can't enter it without both passwords. Continue onward searching for the Sapphire on Six Island and see if you can come across the other secret code.

Location: Dotted Hole

Method:
In the ancient ruins of Six Island, there is a chamber that requires you use Cut on the door to enter. Complete the puzzle by falling through the top hole, then the left, then right, then down. You will find the Sapphire on the bottom floor - but it seems you were followed! An agent working for Team Rocket will snatch the Sapphire from your hands then head off back to Five Island to sell it at the Rocket Warehouse. Before he leaves however he will give you the second password, enabling you to raid the outlet.

Location: Five Island / Rocket Warehouse

Method:
Now that you have both passwords you can defeat Team Rocket once and for all. In this secret hideout you will find Team Rocket up their usual nefarious tricks, including hoarding stolen Pokemon and researching how to force evolution. The puzzles in here are similar to the hideout in Celadon City and the Viridian City Gym. This time you'll fight two admins in lieu of Giovanni, as well as Gideon, who is hanging around with the Sapphire in his possession.The first Rocket Admin uses three Poison-types you've seen in other major battles from the game. Be careful though as her Pokemon have powerful movesets.After the path to the main office is switched on, you can fight the second Rocket Admin. His team is a bit different, using the Pokemon Houndoom as his main powerhouse. After being defeated, the Admin will recognize your Earth Badge and learn what's happened to Team Rocket.

After you've beaten Gideon, Team Rocket will be finished for good in the game. However, they return in the 2009 games Pokemon HeartGold and SoulSilver, so play those next to learn the true fate of Team Rocket.