There are several different methods of automating a bilge pump. One is to use a float switch that uses a float or hinged paddle to turn the pump on (i.e. complete the electrical circuit) when the water reaches a certain point. The "Rule-a-matic" float switch is very common. Another style uses air pressure. Then there are automatic bilge pumps that don't use a float switch at all, they run every few minutes and shut off when they detect no more water to pump (which hopefully is 99+% of the time).
There's a good chance that you have something as simple as a stuck float. They get coated in whatever is floating in and on your bilge water. Most have way to manually manipulate the float - it might be to lift the hinged paddle directly, or if the float is encased, a little knob to move the float up and down. Look for a float within a few inches of the pump, or follow the wires out of the pump to where they are spliced into the power supply (probably no more than 24"), you may find a set of wires that run to the float switch coming out of this same splice.
Good luck
Dan
