Fishing Derby is just an infinite fishing game. Press the arrow keys to move the fishing line and hold the down arrow key to move the line downwards faster, because the line gradually sinks. Once you are touching a fish with the line, press the up arrow key. While you are reeling in the fish, use the arrow keys to move the line out of the shark's reach. If the fish touches the shark, you lose a point.
Credit to Activision for the original game some 50-40 years ago.