After beating Misty in the Cerulean Gym, you’ll want to heal up your Pokémon at the Pokémon Center, if necessary, and then make your way to the house in the northeastern part of town that was blocked by a police officer.
You’ll now see a Squirtle run off with the officer’s Poké Ball, forcing her to chase after it and stop guarding the entrance to the house that was broken into, leaving you free to enter.
Inside the house, you’ll notice it’s a wreck, and your partner Pokémon will investigate the house until it finds some berries in a basket, which distracts its attention. It then finds a gigantic hole in the side of the house.
By talking to the people inside, you’ll find that their TM for the move Dig was stolen by Team Rocket. Head outside and you’ll find the Team Rocket Grunt responsible for the break in. Talk to him and you’ll start a battle with him.
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Raticate is an evolved Pokémon that is capable of hitting fairly hard, so watch out. It has Super Fang, which cuts the target’s HP in half of whatever it currently is, and then also has Quick Attack to follow up with.
After beating the Team Rocket Grunt, he’ll return the TM he stole, giving you TM10 Dig before running off. You don’t have to give it back to the man inside the house; talk to him and he’ll say you can keep it.
Dig is a great TM for most Pokémon that can learn it, as it’s a solid 80-power Ground-type move, and a surprising number of non-Ground-type Pokémon can learn it. Just keep in mind that it takes one turn of digging underground, where the user in generally invulnerable, before the attack lands, so you’ll need to time it right. Most of the time that isn’t an issue, though.
Your Pokémon might find a Razz Berry hidden beneath the nearby bench, so check that out, and then proceed south, avoiding the ledge that’s directly south and opting for the fenced-in path instead.
Follow that path all the way until it turns west, then keep following the path, past the ledges, to find a Burn Heal.
Going further south will lead you onto Route 5, but your best bet is to hop down the ledges so you can access the patches of grass on the route that contain Pokémon.