What is the model number and does it turn on manually? If it turns on manually, you know at least that the pump motor is working.
In terms of the automatic feature, first check to be sure current is getting to the pump. I believe the automatic feature uses a different current source than the manual switch so just because it turned on manually doesn't mean there isn't a problem with the current source for automatic operation. If current isn't getting to the pump on this circuit, the answer may be as easy as replacing a bad fuse. Assuming it is getting current, then check the automatic switch. That should cause it to turn on unless there is a problem with the float switch or pump motor.
One type of automatic switch turns on and senses the current drawn by the motor. If the current draw is low, it assumes there is no water to pump and turns off. I've seen some disparaging remarks about the longevity of this methodology, but I don't have this type on my boat.
The other type of automatic switch uses a float. The latter is easy to test simply by unsnapping the pump from its housing and pushing up on the float.
This is a starting point for you.
Bill
Edgewater, MD