After you get your starter pokémon, you go with Bianca to Route 19. She will show you how to catch pokémon. After that, you have to find Hugh.
Learn How to Catch Pokémon
When you go north through the gate, the gatekeeper lady will give you a potion.
Continue north to find Bianca, who will reminisce about when she started her adventure on Route 1 two years ago.
Then she encounters a wild pokémon. She will show you how to catch it. Just lower its HP, then use a Pokéball from your bag to try to catch it. You don't have to press any buttons while she battles the pokémon. Just watch. Afterward, she mentions that if you can paralyze a pokémon or make it sleep, it will become easier to catch.
After that, she will tell you to go east toward Floccesy Town to find Hugh and give him the Town Map. Then she will return to Aspertia City.
Catch Some Pokémon and Go East
In the grass in this area, you can find Purrloins and Patrats. I recommend catching at least one of each.
If you want, you can go back to the Pokémon Center in Aspertia City to heal up.
Near the east side of Route 19, there is a pokéball in the grass. It contains a potion.
When you go east some more, Alder will talk to you and say that he wants to help you train your pokémon. Then he goes east.
Follow him east to Floccessy Town.