Okay, so, it was a year later after Aang took down the Fire Lord, or Suprime Ruler, and Zuko wanted to know where his mother was after some boring lecture guy said family is important to leaders. So he went to the prison that was holding Ozai and Azula, and asked Azula where she was. Azula then agreed to help him find her, but they had to make a deal. The deal was that she could come with them, making it very awkward for Aang, Katara, Sokka, and Zuko (and, sadly, Toph did not go).
At that point, Aang and Katara were dating, and pretty much being with each other on the way to a small Fire Nation town where Ursa was raised. When they got there, a giant wolf spirit attacked them, and Azula defeated it. During the night, Zuko found his feelings for his sister, and wanted to give her a blanket, till he found a note written by Ursa which stated that he was not Fire Lord Ozai's son, but Ursa's ex-boyfriend's son.
The next morning, Azula saw that the note was missing, and attacked Zuko for it. Aang stopped her, and then they went to the town.
When they got there, they met a sweet woman and her family. She had a husband and a daughter. They gave them food and then they went to a certain forest, where you can find the Mother of Faces, which is where you can completely change your identity, and maybe even your memory.
Then they eventually meet the Mother of Faces, and Azula asked her where Ursa was. The Mother of Faces said the woman they were with before was Ursa, and that she had changed her identity so that she could be with her boyfriend. Azula came to actually kill Ursa, because she was going crazy and seeing her in places where she was alone.
So then, the Mother of Faces was kind enough to give Ursa's REAL face back, and memory, so Ursa remembered Zuko and Azula.