Since Lavendar Town comes after Vermillion in the game, I'm assuming you don't need directions, just a list of what to do to get further in the game.
Once you've done everything in Vermillion, go through Diglett's Cave. Now you can use Cut, so go south on the new route, use Cut on the tree, and now you can get into a building which has one of Professor Oak's aids in it. He'll give you the Flash HM if you have at least 10 Pokemon in your 'Dex.
Return to Cerulean City, and now you can go through Rock Tunnel, exiting the other side in Lavendar Town.