Instructions
Take Route 42 all the way west from Mahogany Town until you hit Ecruteak City. Route 42 is located between Mahogany Town and Ecruteak City. You will need a Pokémon who knows Surf to get through Route 42, as it is separated by two small lakes.
Go north on Route 39 and enter Route 38 to the east. Take Route 38 all the way east to enter Ecruteak City. You can access Route 39 by going to Olivine City and taking the northern exit.
Travel to Violet City and take the western exit to enter Route 36. Go northwest on Route 36 to enter Route 37. Go north through Route 37 to enter Ecruteak City.
Travel north on Route 35 from Goldenrod City and enter Route 36 to the east. Take Route 36 northeast to enter Route 37. Head north through Route 37 to enter Ecruteak City.
Select a Pokemon who knows the Fly technique and fly to Ecruteak City. Pokemon who know Fly are instantly able to fly you to towns, provided you have already visited those towns at least once before. You will obtain Fly after beating the Cianwood gym leader, Chuck, and it comes in the form of HM02.