Do you have the little cylinder constant spray pump or the piston pulsing style? Usually, if you have a cylinder style pump, it's lack of use that allows them to dry up and crystalize. Thus, no workee when you go to use it. If you hear NO HUMMING from the pump when you try and use the squirters, you're not turning the motor. If it hums and nothing happens, try cleaning out the lines before and after the pump. Or you may not have enough fluid in the lines and it may just take a minute for it to start pumping out.
The piston style may need rebuilding, or new rubber valves. Or possibly more work? I don't know. It's more mechanical, so it should be turning if your motor is running and you click in the washers.
Going off memory here, but for the round cylinder pump, there is a small metal clip with a tag holding the cylinder pump on the motor cover. The way its situated, it's probably easiest to just take the wiper motor off the car first to reach the clip. A few bolts and some wires and it's off. The pump is PITA to get out, but once the clip is out the pump should be able to come out of its seat where it plugs into the motor cover. 99% of the time, the pump end is simply clogged up solid with crystalized washer fluid and won't turn because the impeller is clogged up. It's just a little rubber star impeller in there.
You could soak the business end of it in hot water for a little bit and see if you can get it to loosen up. I have disassembled them before and got them to work again (brush springs can fly out so watch out for that if you take it apart). But now I've got a slew of NOS ones if that sh*t happens I'll just swap in a new one.
