Screen cleaner is used during a print run and after you've done your last print.
With waterbased inks you can use water and fairy liquid after printing however screen cleaner will accelerate the clean up and help any of those tough bits without damaging the stencil.
Its best use one or the other and not mix the two methods. This can damage the emulsion. During printing screen wash dries faster so you can get back to printing quicker.
We often use water & fairly liquid when we have finished printing but have the screen wash on the side and use it for the more difficult and stubborn bits!