The central city of the Kanto region can be reached via four directional gatehouses–located at the end of Route 5, Route 6, Route 8 and Route 7. The easiest way is probably via Route 7, coming from Celadon City. To get through the gatehouses, you will need the Tea from Brock at the front of the Celadon City Condominiums.
Assuming you come from Route 7, you’ll start off near the west side. To begin with, head north towards the north-west corner of the city. There should be a Rocket Grunt, but he’s too busy to battle you. Go past him and enter the first house along the top. Go upstairs and show a Clefairy (from Mt. Moon) to the Copycat.
She’ll reward you with TM08 Substitute. This tricky move cuts your Pokémon’s HP by a quarter, but produces a decoy with the amount of HP that it expended. It can be used to avoid damage that exceeds a quarter of your HP and protects you from status conditions too. Also, search above her bed for a hidden Moon Stone.
Back outside, follow the road east towards the north-east corner of the city. Here, there are two Gym-like buildings. The one on the right, which is currently blocked by a Rocket Grunt, is where the official Gym is. Meanwhile the one on the left is the Fighting Dojo. If you have a strong Psychic, Flying or Fairy-type, or you trust in your skills, feel free to enter.
Meanwhile, past the main Gym is a policewoman. If you walk behind the Gym signpost and behind the tree, you can head right and grab the X Sp. Def in the far corner. After that, follow the eastern road south. Opposite the east gatehouse is the Poké Mart. If you’re here to liberate Silph Co., you should stock up on supplies while you can.
To the right of the Poké Mart is a Trainer Fan Club, although there’s nothing there besides gossip. Continue south to the next street along. In the center of this street is the entrance to Silph Co. If you beat Jessie and James atop the Pokémon Tower, they will open the way to Silph Co. There’s still a bit more to visit before going inside though.
Make your way to the southern-most street, for example by continuing west from the Silph Co. street, then heading south. Near the south-west corner is the city’s Pokémon Center.
Speaking of, continue towards the south-east corner of the city. Over here, there’s a man who will pre-emptively give you TM40 Psychic.
Definitely teach this to your Psychic-types, as it’ll come in useful against the Poison-types used by Team Rocket and the upcoming Gym in Fuchsia City. Plus the Fighting-types used by the Fighting Dojo in this city. Finally, when ready, enter Silph Co.