Just trace the hoses back from the squirt nozzles and you'll find the pump. GM in that era usually had a pump that is held into the bottom of the plastic fluid tank by a rubber grommet.
As others have mentioned, make sure first that it's the pump rather than a clogged nozzle, or a hose that has come off and is dutifully squirting into some random place under the hood, or the electricity supply to the pump motor.
The pump is an easy repair (depending on how hard it is to access that part of the tank on your model and year). All the auto parts stores would have replacements; it's a common generic part (and a fairly fallible one, in my experience).
Note that the instructions that come with the new pump may tell you how to prime it. Running dry for very long isn't good for them.
If the pump has to come out, you can also use the garden hose to chase out whatever dirt and algae are sitting in the reservoir.
Cheers,
--Joe