After walking through the soot-covered route 113 and collecting ash for the Glass Workshop, you proceed west to Fallarbor Town.
In the Pokémon Center, talk to the woman in front of the PC to meet Lanette, the inventor of the PC system. Lanette lives on Route 114 and asks you to meet her there.
Check the crater in the bottom left of town to find a hidden Nugget.
In Fallarbor Town you can find the Move Tutor, who will teach a pokémon any move that it could have learned when leveling up from level 1 to its current level. You have to give the Move Tutor a Heart Scale to teach a pokémon a move. You can get Heart Scales in various places. Later you will also encounter a type of pokémon that sometimes carries Heart Scales.
When you are ready to move on, go west to reach Route 114.