Some Move Tutors will teach the player's Pokémon moves for free. However, there are typically conditions on which Pokémon can learn the moves they offer.
Located shortly after the second Gym, an old woman lives alone. She will speak to the player and ask to see their Pokémon. If any of the Urobos starter Pokémon (or their evolutions) are present, she will teach them one of three moves depending on that Pokémon's type. These moves, if used in combination with each another in double battles, will produce additional effects.
In [location] City is a building to the north with a strange man. He will speak gibberish and brag about his many adventures and wonderful encounters. If the player listens to his story, the man will thank the player and teach one of their Pokémon a Normal-type move.
Located on Route [x] is a small house. This is the home of a young boy and girl, who are revealed to be siblings. After a short chat, the boy will gladly teach the player's starter Pokémon one of three ultimate moves depending on its type, but only if the Pokémon is fully evolved and is completely happy. The young girl will teach any Dragon-type Pokémon the move Draco Meteor, but only if it is completely happy.