From Nookipedia, the Animal Crossing wiki
Tortimer will preside in the Plaza and no special visitors will be seen except K.K. Slider. Each day, provided the player speaks to him, Tortimer will give him or her a different bag of flower seeds. He will also inform the player which flower represents the month in which they were born if they speak to him repeatedly.
At the end of the week, the winner of the Flower Fest will receive the Flower Trophy for his or her efforts.
It is unknown what the precise requirements are to win the contest. Planting many flowers within three spaces of the player's house allows for a good chance at winning as does planting a well-arranged, varied array of flowers.
Other villagers will plant flowers within two spaces of their houses. Players can cheat by planting patterns all over the neighbor's homes, preventing any flowers from growing and thus eliminating competition. Using this method, the player can win by planting just one flower. Flowers can also be stolen from the town's residents which increases the player's chances of winning the Flower Fest and decreases the villager's hopes.