What do you do in Celadon City?

you have to use surf from fushia city and go the long way but once you get there after wandering around in buildings there will be a woman that gives you a tea you can then go to any guard and get...

I believe you take a boat with an old man

Once at Lavender Town, go on the path to the west of the town. Once at the end of the path go in the underground tunnel.

walk there