After battling your rival and getting the Pokedex from Professor Oak and the egg from Mr. Pokemon, you need to travel north of CherryGrove city. Stick to the left, since last time you couldn't pass due to to kids blocking the way. They have moved now, and go north from there, and take your first left to go to Violet City.
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In Violet City next to the PC in the Pokemon Center
first at sprout tower at violet city. next is burnt tower at ecruteak city.
In HG/SS you trade Shards for Berries. Trade with Jugglers in Violet City and Fuchsia City.
In Violet City, go north and left. Talk to the Hiker to receive the HM.
You can get in Routes 7 (west of Saffron City), 8 (west of Lavender Town), 36 (west of Violet City), 37 (south of Ecruteak City), and 48 (south of the Safari Zone).