Every summer, I dump out whatever is in the washer tank, and fill it with clean water. Then, I run the water through the washer system while I wait. (I disconnected the wipers at first; later on, I rigged a system to run the pump without the wipers working.)
This rinses out all the dried-up and coagulated washer fluid from the system. The nozzles usually gather a lot of cruddy blue-green stuff around them. Like John said, using a pin helps to clean them out, too.