After you get the Thunder Badge from Lt. Surge, you can go into Diglett's Cave, east of Vermilion City.

Travel Through the Cave

Diglett's Cave is east of Vermilion City. Go in and go down the ladder. In this area, you can encounter wild Diglett, Dugtrio, Zubat, and others.

Go northwest until you reach a ladder. Go up, then go outside. You will be in Route 2. Go south to meet one of Professor Oak's assistants. Go into his house, and your partner pokémon will learn the Secret Technique Light Up.

When you go back outside, your rival will be there, and will offer to take you to a place where you can use the new Secret Technique you learned. If you say yes, you and your rival will go to Cerulean City, and your rival says to go east to find Rock Tunnel, where you can use the Secret Technique Light Up.

Go east from Cerulean City, cut down the small tree, and go east to Route 9.