From Nookipedia, the Animal Crossing wiki
Serena is a solid white chihuahua with a white toga. She has large beady eyes and wears golden jewelery. On her head, she wears a veil, and also has large pointed ears in front. She is often mistaken for an angel.
To see Serena, the player must first unlock the fountain by donating 400,000 Bells (in addition to the 200,000 Bells that are needed for the extra bridge) to the Town Fund. Then after the fountain is built, the player must throw an axe into the fountain by swinging the Wii Remote in a horizontal swipe in front of their body. Doing so will throw the axe into the middle of the fountain. It should be noted that the day the fountain is opened, Tortimer will be in the way, preventing the player from summoning Serena. Serena may come out and ask any combination of 3 different questions, which will lead to further questions. Usually she will appear disappointed after the player throws the axe in, after questioning she may give the player a gold axe, a silver axe, return the basic axe or she might just keep the player's axe and give them nothing. There is a statue of her in the center of the fountain in the City.
Getting the Silver/Gold Axe
Serena is very unpredictable and often gets mad when axes are thrown at her. Sometimes, she asks if she appears "goddess-y" and asks for the player's opinion. If the player sweet-talks Serena enough, she may give the golden axe. However, the player may get the axe through telling the truth.
Sometimes, Serena has a sad face and asks "Why are you throwing axes at me? Do you hate me?". If the player says yes, she might keep their axe or she might give them a gold axe so they would like her. If the player says no, she might get mad at them and throw the axe, tearing her favorite toga.
There are many other questions Serena may ask. She is very unpredictable, and also is a chronic liar, as she may say that she will give the player a gold or silver axe but never actually gives it. Serena has a lot of axes at times, but other times she has "run out" of gold/silver axes.
She also sometimes asks, "Did you throw in a golden axe, or maybe it was a silver axe?", referencing an old story where a man drops his axe into a river and a spirit/mermaid asks the same thing (The man told the truth and got both, but since Serena is how she is, the player may not get the same result).
As a final question, Serena will sometimes ask the player if they want a "present". If the player says yes, Serena will ask them to pick a hand (saying no will result in her taking the player's axe). If the player chooses the right, Serena may take the player's axe, return it or give them a gold/silver one. Picking left has the same function, but Serena might only give the player a silver axe.
In Animal Crossing: New Leaf, peppy villagers may reference Serena and City Folk's method of obtaining the silver and gold axes in conversation. They'll ask, "if you dropped an axe in a magic pool, (player)...and a goddess appeared and she said she'd transform it for you, which one would you choose?"
Serena appears as a spectator in the Town and City stage, and as a collectible trophy.