1) Go through Diglett's cave, and get HM Flash from one of Oak's Aides in one of the houses in the previously inaccessible areas of Route 2. Head back to Vermillion City.
2) Clear the S.S. Anne and get HM Cut, if you haven't already done this. The ticket comes from Bill on Route 24.
3) Go back to Cerulean City, and then go into the house that was previously blocked by a police officer. Go through and fight the Rocket in the backyard, he will give you TM Dig. After that follow the path east onto Route 10. You will need Cut to access this route.
4) After getting past Route 10, teach somebody Flash, heal up at the Pokemon center, then head through ROCK TUNNEL, not Diglett's Cave. You will need Flash to navigate this area. There are a lot of trainers and Pokemon in here, so be careful. You'll need a Water type, a Fire type, and a Fighting type on your team, as the bare minimum.
5) After getting out of Rock Tunnel, head south. You'll find yourself in Lavender Town.
Hope that helped.
Beat the Kanto games... 4 times.