This happened during the final episodes of Book Two: Earth, specifically when Appa was lost from the group.
The Kyoshi Warriors, while picking berries, noted traces of Appa's fur in the bushes. They followed the trail, found Appa and took care of him. However, while with Ty Lee and Mai looking for the Avatar, Azula noted the trail of Appa's fur as well. This led her to the Kyoshi Warriors, and eventually, to a fight.
Ty lee and Mai quickly took the upper hand against the Kyoshi Warriors, and Azula presumably defeated Suki by herself. Suki was then sent to the Boiling Rock, being the leader, while the other warriors were taken to another Fire Nation prison cell.