The water pump is commonly known as the pump which pushes the coolant around the head and engine block.
The pump you are referring to is the windscreen washer motor.
The most basic thing first... does the reservior/bottle have water in it??
The bottle might have gunk/dirt inside it, blocking a small filter which might be at the mouth of the motor. Look inside the bottle when empty.
The rubber hoses to the squirt jets might be kinked or not connected.. check the hoses all the way to the jets.
Lastly, the jets might be blocked.. not uncommon if the car has been polished recently, as the polish can easily block the small holes. Using a small pin can fix blocked jets.
To check if the jets are at fault, disconnect the hose to the jets, and see if you can get water pumping out of the hose with someone operating the switch... then work backwards.
In the end, it could still be a weak/faulty motor.
Goodluck
Aussie John, June 2008