There are several game modes in Harvest Moon: Frantic Farming. The first is the story mode, which can be completed with a variety of different characters with more of the story being revealed each time. In story mode there are a number of cut scenes interspersed with puzzles to get though.
The puzzle in Harvest Moon: Frantic Farming is the same every time, but with different goals. You have to farm a field with the help of a sprite. The veggies can be moved so he can pick them and continue to water the field at the same time. Once he runs out of mature veggies to pick it is game over.
In story mode you usually have to pick a certain number of vegetables or reach a certain score. Each time you pass story mode with a new character something new is unlocked.
Harvest Moon: Frantic Farming also has a multiplayer option in which you can battle a friend for the high score. They don't even need the cartridge to play.
There is also a mission mode and a score attack mode, but neither of them are very interesting.