Assuming you have a standard windshield washer system, testing the windshield washer pump is relatively easy. All you need is a clean cup or bowl, some water and a voltage meter.
First, locate the windshield washer fluid reservoir. It should be near the front of your vehicle and clearly labeled. Once you've found it, remove the cap and fill the reservoir with water.
Next, turn on your ignition but don't start the engine. With the ignition on, activate your windshield wipers and then hold down the button that activates the windshield washer fluid spray. If your pump is working properly, you should see a steady stream of fluid being sprayed onto your windshield.
If there's no fluid coming out at all, or if it's coming out in spurts rather than a steady stream, then your pump may be faulty and will need to be replaced.
To test for an electrical problem, use a voltage meter to check for power at the connector on top of the pump motor. If there's no power present, then you'll need to trace back through your wiring to find where the break is occurring.