Rhyanna had a Pokemon battle with her younger brother in which she defeated his Murkrow fairly easily. He didn't like the fact that he was defeated so easily and got mad at his sister.
Rhyanna first encounter Ash and his friends as they were being affected by Murkrow and were seeing things in a forest just near the village that she lives in. They thought they were swimming until she snapped them out of it.
Rhyanna explained that she was looking for a Dusk Stone and Brock decided that she would go with her to help her find it. With the help of her Misdreavus, Brock found the Dusk Stone under a large rock.
Team Rocket showed up and tried to take the Dusk Stone and her Misdreavus. Brock's Sudowoodo was unable to defeat the large mecha and it captured Rhyanna, Misdreavus and the Dusk Stone. It wasn't until Mitchell arrived that she was rescued.
The character's Japanese name is taken from the character Tyltyl in Maurice Maeterlinck's The Blue Bird, which her episode was heavily based on.